AP Calculus BC Easy practice

Using the limit definition, find $f^{\prime }(x)$ for $f(x)=3x^2-5$.

Find $\frac{d}{dx}\left[x^3\ln x\right]$ for $x>0$.

A spherical balloon is inflated so its radius increases at $0.5$ cm/min. How fast is the volume increasing when $r=3$ cm?

Evaluate ${\lim }_{x\to 0}\frac{e^x-1-x}{x^2}$ using L'Hôpital's Rule.

For $g(x)=x^4-8x^2$, use the Second Derivative Test to classify $x=0$ and $x=\pm 2$.

A solid has a square cross-section perpendicular to the $x$-axis, with the base region bounded by $y=\cos x$ and $y=0$ on $[-\pi /2,\pi /2]$. Find the volume.

Does the alternating series $\sum _{n=1}^{\infty }\frac{(-1{)}^{n+1}}{n^2}$ converge?

Find the volume of the solid formed by revolving $y=\sqrt{x}$ on $[0,4]$ around the $x$-axis using the disk method.

Using the Left Riemann Sum with $n=4$ equal subintervals, approximate ${\int }_0^2{x}^{2}dx$.

The logistic growth model is $\frac{dP}{dt}=0.3P\left(1-\frac{P}{1000}\right)$. As $t\to \infty$, what does $P$ approach?

Find the average value of $f(x)=2x+1$ on $[1,4]$.

A particle moves along the $x$-axis so that its position at time $t\ge 0$ is $x(t)=t^3-6t^2+9t$. At what times is the particle at rest?

Does the $p$-series $\sum _{n=1}^{\infty }\frac{1}{n^{3/2}}$ converge or diverge?

A curve is given parametrically by $x(t)=t^2-1$ and $y(t)=2t$. Find $\frac{dy}{dx}$ in terms of $t$.

Find the area of the region bounded by $y=x^2$ and $y=2x$.