Practice Test 4 - AP Calculus BC

20 questions. Answer them in any order, then submit to see your score and every explanation.

The position of a cart is modeled by $s(t)=4t^5-3t^2+7t-9$ . What is $s'(t)$ ?
An intensity function is $F(t)=2\sin t+\ln t$ . What is $F'(t)$ ?
A rectangular prism has a square base and must have total surface area 150. To maximize volume, what should be maximized?
What integral gives the volume if the base is bounded by $y=\ln(x)$ and $y=0$ for $1\le x\le e$ , squares perpendicular to the $x$ -axis?
For $f(x)=\sin x$ , using $P_5(x)=x-\frac{x^3}{3!}+\frac{x^5}{5!}$ to approximate $\sin(0.4)$ and $|f^{(6)}(x)|\le 1$ on $[0,0.4]$ , what is the maximum error?
For $x>0$ , compute $\int \frac{\ln x}{x^2}\,dx$ using integration by parts.
Consider $\sum_{n=1}^{\infty} \left(\frac{2n-1}{2n}\right)$ . What does the nth-term test imply?
Let $g(x)=\frac{1}{(x-2)^2}$ . What type of discontinuity does $g$ have at $x=2$ ?
In a lab, concentration is modeled by $C(t)=\dfrac{t^2+3t}{t+1}$ . What is $C'(t)$ ?
A long-run average uses $\int_{1}^{\infty} \frac{1}{x(\ln x)^2}\,dx$ ; determine convergence and the integral's value.
A sequence of adjustments uses $sum_{n=1}^{infty}frac{2^n}{3^n+n}$ . Which comparison determines convergence?
A company models demand as $D(p)=(10-p)(p^2)$ . What is $D'(p)$ ?
At $x=0$ , $a'(0)=0$ and $a''(0)=4$ ; how is the critical point at $x=0$ classified?
A savings balance satisfies $\frac{dB}{dt}=0.05B$ with $B(0)=1000$ . Find $B(2)$ .
For $u(x)=\frac{1-\cos x}{x^2}$ , which expression represents the behavior as $x$ approaches $0$ ?
Set up the area between $x=6+y$ (right) and $x=2y+1$ (left) on $-1 \le y \le 1$ .
Which integral gives the area enclosed by $r=2\sin\theta+2$ for $0\le\theta\le2\pi$ ?
For $\dfrac{dy}{dx}+y=x$ , does $y=x-1+Ce^{-x}$ satisfy the differential equation for any constant $C$ ?
For $p(x)=x^4\ln(x)$ with $x>0$ , what is the second derivative $p''(x)$ ?
A particle's position is $s(t)=4\sin t-3t^2$ . What is $s'(t)$ ?

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