Sample Calculus Problems: Get College Ready!

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Calculus and Analysis

Recent questions in Calculus and Analysis

phumzaRdY 2022-11-28

A playground merry-go-round of radius R=2 m has a moment of inertia I=250 kgm^2 and is rotating at 10 rev/min about a frictionless, vertical axle. Facing the axle, a 25 kg child hops onto the merry-go-round and manages to sit down on the edge. The new angular speed of the merry-go-round is
A.10 rev/min
B.7.14 rev/min
C.3.14 rev/min
D.8.45 rev/min

ingerentayQL 2022-11-28

Find the dot product, $a \cdot b$
$a \cdot b a = 6 i + 5 j, b = - 5 i + 4 j$
A.50
B.<1,9>
C.-10
D.<-30,20>

Erick Wyatt 2022-11-28

Can you demonstrate the calculation for $18$ divided by $0.18$ - what are the steps, what is the first step?

Simon Hanna 2022-11-28

What is the derivative of $\frac{1}{x}$ ?

unecewelpGGi 2022-11-27

Use Euler methed to estimate the value of ( 2 loops), where $y$ is the solution of the initial value problem $y^{'} = 1 - 2 x y, h = 0, 1, y (1) = 0.538$

hEorpaigh3tR 2022-11-27

Find and classify critical points of $f (x, y) = \cos (x^{2} + y^{2})$
I have to classify the critical points of f, but the problem says to only consider the points $(0, 0), (\sqrt{\frac{π}{2}}, \sqrt{\frac{π}{2}})$
So, long story short, after using the second derivative test I got that $D = 0$ at both critical points.
How should I proceed with this problem?

jastukudYb 2022-11-27

What is the derivative of $\tan 2 x$ ?

VarceprewN3M 2022-11-26

Describe the vertical asymptotes) and holes) for the graph of $y = \frac{(x + 2) (x + 4)}{(x + 4) (x + 1)}$
A. asymtotes: x=-1 and hole: x=4
B. asymtotes: x=2 and hole: x=-1
C. asymtotes: x= -1 and hole: x=-4
D. asymtotes: x=1 and hole: x=4

Ernesto Wagner 2022-11-26

We need to know which of the followingis incorrect?
The derivative of $\sqrt{n} + \frac{1}{\sqrt{n}}$

Erick Wyatt 2022-11-26

At what point does the curve have maximum curvature?
$y = 5 \ln (x)$
$(x, y) = (,)$
κ(x) approaches ________ as $x \to \infty$ ?

armlanna1sK 2022-11-26

Calculate the double integral.
$\int \int \frac{6 x}{1 + x y} d A, R = [0, 6] \times [0, 1]$

E Laurie2022-11-25

Justine Pennington 2022-11-25

What is $δ S$ and $δ H$ ?

nuseldW4r 2022-11-25

Which of the following statements is true for the function
f(x)=x 2 +x−6 2x 2 −2 ?
a)
y=1 2 is a horizontal asymptote and x=2 is a vertical asymptote.
b)
y=1 2 is a horizontal asymptote and x=1 is a vertical asymptote.
c)
y=3 is a horizontal asymptote and x=-1 is a vertical asymptote.
d)
y=3 is a horizontal asymptote and x=2 is a vertical asymptote

klupko5HR 2022-11-25

What is the derivative of $x y$ ?

vegetatzz8s 2022-11-25

How can I solve this differential equation? : $x y d x - (x^{2} + 1) d y = 0$

klupko5HR 2022-11-25

Find the inverse Laplace transform of $\frac{s^{2} - 4 s - 4}{s^{4} + 8 s^{2} + 16}$

phumzaRdY 2022-11-25

How do i find the lapalace transorm of this intergral using the convolution theorem? $\int_{0}^{t} e^{- x} \cos x d x$

hemotropS7A 2022-11-25

How to find inverse Laplace transform of the following function?
$X (s) = \frac{s}{s^{4} + 1}$
I tried to use the definition: $f (t) = L^{- 1} {F (s)} = \frac{1}{2 π i} lim_{T \to \infty} \int_{γ - i T}^{γ + i T} e^{s t} F (s) d s$ or the partial fraction expansion but I have not achieved results.

unecewelpGGi 2022-11-25

What's the correct way to go about computing the Inverse Laplace transform of this?
$\frac{- 2 s + 1}{(s^{2} + 2 s + 5)}$
I Completed the square on the bottom but what do you do now?
$\frac{- 2 s + 1}{(s + 1)^{2} + 4}$

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