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Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

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6 Diagnostic Tests 373 Practice Tests Question of the Day Flashcards Learn by Concept

Example Questions

Example Question #213 : Vectors And Vector Operations

Given the vectors

$\small \small \small \small v=\left(\frac{1}{2},2\right)$

$\small \small \small \small w=\left(\frac{1}{4},-5\right)$

find the sum $\small v+w$ .

Possible Answers:

$\small \small \small v+w=(3/4,3)$

$\small \small \small v+w=(5/8,-3)$

$\small \small v+w=(3/4,-3)$

$\small \small \small v+w=(3/4,2)$

Correct answer:

$\small \small v+w=(3/4,-3)$

Explanation:

Given the vectors

$\small \small \small \small v=\left(\frac{1}{2},2\right)$

$\small \small \small \small w=\left(\frac{1}{4},-5\right)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small \small v+w=(1/2,2)+(1/4,-5)=(1/2+1/4,2-5)$

$\small =(3/4,-3)$

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Example Question #214 : Vectors And Vector Operations

Given the vectors

$\small \small \small \small \small \small v=(-1,2,\pi^2)$

$\small \small \small \small \small \small \small w=(1,-2,\pi)$

find the sum $\small v+w$ .

Possible Answers:

$\small \small \small \small \small \small \small v+w=(0,0,\pi(\pi-1))$

$\small \small \small \small \small \small \small \small v+w=(0,0,\pi(1-\pi))$

$\small \small \small \small \small \small v+w=(0,0,\pi(\pi+1))$

$\small \small \small \small \small \small \small v+w=(-2,-4,\pi(\pi-1))$

Correct answer:

$\small \small \small \small \small \small v+w=(0,0,\pi(\pi+1))$

Explanation:

Given the vectors

$\small \small \small \small \small \small v=(-1,2,\pi^2)$

$\small \small \small \small \small \small \small w=(1,-2,\pi)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small \small \small \small \small v+w=(-1,2,\pi^2)+(1,-2,\pi)=(-1+1,2-2,\pi^2+\pi)$

$\small \small \small \small \small =(0,0,\pi(\pi+1))$

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Example Question #11 : Vector Addition

Given the vectors

$\small \small \small \small \small \small \small v=(\ln 2,1/2,e^2)$

$\small \small \small \small \small \small \small \small w=(e,-1/4,e^4)$

find the sum $\small v+w$ .

Possible Answers:

$\small \small \small \small \small v+w=(\ln 2-e,3/4,e^2-e^4)$

$\small \small \small \small \small v+w=(e^2,1/4,e^2-e^4)$

$\small \small \small \small \small v+w=(1/4,e^2+e^4,\ln 2+e)$

$\small \small \small \small v+w=(\ln 2+e,1/4,e^2+e^4)$

Correct answer:

$\small \small \small \small v+w=(\ln 2+e,1/4,e^2+e^4)$

Explanation:

Given the vectors

$\small \small \small \small \small \small \small v=(\ln 2,1/2,e^2)$

$\small \small \small \small \small \small \small \small w=(e,-1/4,e^4)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small v+w=(\ln 2,1/2,e^2)+(e,-1/4,e^4)=(\ln2+e,1/2-1/4,e^2+e^4)$

$\small \small \small =(\ln 2+e,1/4,e^2+e^4)$

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Example Question #12 : Vector Addition

Given the vectors

$\small \small \small \small \small \small \small \small v=(1,-1,-2)$

$\small \small \small \small \small \small \small \small \small w=(0,-1,5)$

find the sum $\small v+w$ .

Possible Answers:

$\small \small \small \small \small v+w=(2,-1,3)$

$\small \small \small \small \small v+w=(1,2,-3)$

$\small \small \small \small v+w=(-1,2,3)$

$\small \small \small \small v+w=(1,-2,3)$

Correct answer:

$\small \small \small \small v+w=(1,-2,3)$

Explanation:

Given the vectors

$\small \small \small \small \small \small \small \small v=(1,-1,-2)$

$\small \small \small \small \small \small \small \small \small w=(0,-1,5)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small \small v+w=(1,-1,-2)+(0,-1,5)=(1+0,-1-1,-2+5)$

$\small \small \small \small =(1,-2,3)$

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Example Question #13 : Vector Addition

Given the vectors

$\small \small \small v=(5,5)$

$\small \small \small \small \small \small \small \small \small \small w=(4,2)$

find the sum $\small v+w$ .

Possible Answers:

$\small \small \small \small \small \small v+w=(7,9)$

$\small \small \small \small \small v+w=(9,7)$

$\small \small \small \small \small v+w=(9/2,7)$

$\small \small \small \small \small v+w=(-9,7)$

Correct answer:

$\small \small \small \small \small v+w=(9,7)$

Explanation:

Given the vectors

$\small \small \small v=(5,5)$

$\small \small \small \small \small \small \small \small \small \small w=(4,2)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small \small \small v+w=(5,5)+(4,2)=(5+4,5+2)$

$\small \small \small \small \small =(9,7)$

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Example Question #14 : Vector Addition

Given the vectors

$\small \small \small v=(-1,-5)$

$\small \small \small w=(1,3)$

find the sum $\small v+w$ .

Possible Answers:

$\small \small \small \small \small v+w=(0,-2)$

$\small \small \small \small \small \small v+w=(5,1)$

$\small \small \small \small \small v+w=(-2,2)$

$\small \small \small \small \small \small v+w=(-2,0)$

Correct answer:

$\small \small \small \small \small v+w=(0,-2)$

Explanation:

Given the vectors

$\small \small \small v=(-1,-5)$

$\small \small \small w=(1,3)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small \small \small \small v+w=(-1,-5)+(1,3)=(-1+1,-5+3)$

$\small \small \small \small \small =(0,-2)$

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Example Question #221 : Vectors And Vector Operations

Given the vectors

$\small \small \small \small \small v=(0,1,\pi)$

$\small \small \small \small \small \small w=(0,\sqrt{2},3)$

find the sum $\small v+w$

Possible Answers:

$\small \small \small \small \small v+w=(0,\pi+3,1+\sqrt{2})$

$\small \small \small \small \small \small v+w=(0,3+\sqrt{2},\pi+1)$

$\small \small \small \small v+w=(0,1+\sqrt{2},\pi+3)$

$\small \small \small \small \small \small v+w=(0,\sqrt{2}+\pi,4)$

Correct answer:

$\small \small \small \small v+w=(0,1+\sqrt{2},\pi+3)$

Explanation:

Given the vectors

$\small \small \small \small \small v=(0,1,\pi)$

$\small \small \small \small \small \small w=(0,\sqrt{2},3)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small \small \small v+w=(0,1,\pi)+(0,\sqrt{2},3)=(0+0,1+\sqrt{2},\pi+3)$

$\small \small \small \small =(0,1+\sqrt{2},\pi+3)$

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Example Question #16 : Vector Addition

Given the vectors

$\small \small \small v=(2,3)$

$\small \small \small w=(4,7)$

find the sum $\small v+w$ .

Possible Answers:

$\small \small \small \small \small \small v+w=(-6,10)$

$\small \small \small \small \small \small v+w=(6,-10)$

$\small \small \small \small \small v+w=(6,10)$

$\small \small \small \small \small \small v+w=(10,6)$

Correct answer:

$\small \small \small \small \small v+w=(6,10)$

Explanation:

Given the vectors

$\small \small \small v=(2,3)$

$\small \small \small w=(4,7)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small \small \small \small \small v+w=(2,3)+(4,7)=(2+4,3+7)$

$\small \small \small \small \small =(6,10)$

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Example Question #11 : Vector Addition

Given the vectors

$\small \small \small \small v=(1/2,4/5)$

$\small \small \small \small w=(5/8,2/5)$

find the sum $\small v+w$ .

Possible Answers:

$\small \small \small \small \small \small \small \small v+w=(9/4,6/5)$

$\small \small \small \small \small \small \small v+w=(9/8,6/5)$

$\small \small \small \small \small \small \small \small v+w=(1/2,6/5)$

$\small \small \small \small \small \small \small \small v+w=(6/5,9/8)$

Correct answer:

$\small \small \small \small \small \small \small v+w=(9/8,6/5)$

Explanation:

Given the vectors

$\small \small \small \small v=(1/2,4/5)$

$\small \small \small \small w=(5/8,2/5)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small \small \small \small \small \small v+w=(1/2,4/5)+(5/8,2/5)=(1/2+5/8,4/5+2/5)$

$\small \small \small \small \small \small =(9/8,6/5)$

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Example Question #21 : Vector Addition

Given the vectors

$\small \small \small \small \small v=(-\pi,\pi^5)$

$\small \small \small \small \small w=(\pi^2,\pi^6)$

find the sum $\small v+w$ .

Possible Answers:

$\small \small \small v+w =(\pi^2,\pi^5)$

$\small \small \small \small \small \small \small \small \small v+w =(\pi(\pi+1),\pi^5(\pi+1))$

$\small \small \small \small \small \small \small \small v+w =(\pi(\pi-1),\pi^5(\pi+1))$

$\small \small \small \small \small \small \small \small \small v+w =(\pi(1-\pi),\pi^5(\pi+1))$

Correct answer:

$\small \small \small \small \small \small \small \small v+w =(\pi(\pi-1),\pi^5(\pi+1))$

Explanation:

Given the vectors

$\small \small \small \small \small v=(-\pi,\pi^5)$

$\small \small \small \small \small w=(\pi^2,\pi^6)$

we can find the sum $\small v+w$ by adding component by component:

$\small \small \small \small=v+w=(-\pi,\pi^5)+(\pi^2,\pi^6)=(-\pi+\pi^2,\pi^5+\pi^6)$

$\small \small \small \small \small \small \small =(\pi(\pi-1),\pi^5(\pi+1))$

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Calculus 3 : Calculus 3

Study concepts, example questions & explanations for Calculus 3

All Calculus 3 Resources

Example Questions

Example Question #213 : Vectors And Vector Operations

Example Question #214 : Vectors And Vector Operations

Example Question #11 : Vector Addition

Example Question #12 : Vector Addition

Example Question #13 : Vector Addition

Example Question #14 : Vector Addition

Example Question #221 : Vectors And Vector Operations

Example Question #16 : Vector Addition

Example Question #11 : Vector Addition

Example Question #21 : Vector Addition

All Calculus 3 Resources

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