Sample Calculus Problems: Get College Ready!

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Calculus and Analysis

Recent questions in Calculus and Analysis

Reeves 2020-11-03

Evaluate the surface integral
$\int_{S} F \cdot d S$
for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation.
F(x,y,z)=xi+2yj+3zk
S is the cube with vertices $(\pm 1, \pm 1, \pm 1)$

BenoguigoliB 2020-11-02

$y + y = e^{- 2 t} \sin t, y (0) = y' (0) = 0$
solution of given initial value problem with Laplace transform

Rivka Thorpe 2020-11-02

Suppose that the plane region D, its boundary curve C, and the functions P and Q satisfy the hypothesis of Greens

kuCAu 2020-11-02

Use the limit definition of partial derivatives to evaluate $f_{x} (x, y) and f_{y} (x, y)$ for the following functions.
$f (x, y) = \frac{x}{y}$

generals336 2020-11-02

Find the Laplace transform $L {u_{3} (t) (t^{2} - 5 t + 6)}$
$a) F (s) = e^{- 3 s} (\frac{2}{s^{4}} - \frac{5}{s^{3}} + \frac{6}{s^{2}})$
$b) F (s) = e^{- 3 s} (\frac{2}{s^{3}} - \frac{5}{s^{2}} + \frac{6}{s})$
$c) F (s) = e^{- 3 s} \frac{2 + s}{s^{4}}$
$d) F (s) = e^{- 3 s} \frac{2 + s}{s^{3}}$
$e) F (s) = e^{- 3 s} \frac{2 - 11 s + 30 s^{2}}{s^{3}}$

he298c 2020-11-02

Solve differential equation $y^{'} + 2 y = y^{2}$

Dolly Robinson 2020-11-02

Use the Laplace transform to solve the given integral equation
$(s) = 2 t^{2} + \int_{0}^{t} \sin [2 (t - τ)] x (τ) d τ$

Bevan Mcdonald 2020-11-02

Give the correct answer and solve the given equation $\frac{d y}{d x} = \frac{y^{2} - 1}{x^{2} - 1}, y (2) = 2$

Ramsey 2020-11-02

Find the linear or affine transformations that satisty the desired properties and write it in the form $T (x) = A x + b :$
The transformation $T : R^{2} \to R^{2}$ sending the origin to itself and a triangle of vertices
$(0, 0), (1, 0), (0, 1)$ to a triangle of verices (0, 0),
$(\sqrt{\frac{2}{2}}, \sqrt{\frac{2}{2}}), (- \sqrt{\frac{2}{2}}, \sqrt{2}) .$

Dottie Parra 2020-11-02

Solve the Differential equations $2 y'' + 3 y' - 2 y = 14 x^{2} - 4 x - 11, y (0) = 0, y' (0) = 0$

aortiH 2020-11-02

Curves to parametric equations Find parametric equations for the following curves. Include an interval for the parameter values. Answers are not unique. The line segment starting at $P (- 1, - 3) and ending at Q (6, - 16)$

pedzenekO 2020-11-01

Solve the Laplace transforms
$\dot{x} - 2 \ddot{x} + x = e^{t} t$
$given t = 0 and x = 0 and x = 1$

Tazmin Horton 2020-11-01

Calculate the Laplace transform
$L {\sin (t - k) \cdot H (t - k)}$

smileycellist2 2020-11-01

Solve the following IVP using Laplace Transform
$y^{'} - 2 y = 1 - t, y (0) = 4$

UkusakazaL 2020-11-01

Give the correct answer and solve the given equation
Let $p (x) = 2 + x and q (x) = x$ . Using the inner product $⟨ p, q ⟩ = \int_{- 1}^{1} p q d x$ find all polynomials $r (x) = a + b x \in P 1 (R) P$
(R) such that {p(x), q(x), r(x)} is an orthogonal set.

UkusakazaL 2020-11-01

What is a parametric curve? $x (t) = t 3$
$y (t) = t$

Kye 2020-11-01

use Green’s Theorem to find the counterclockwise circulation and outward flux for the field F and the curve C. $F = (y^{2} - x^{2}) i + (x^{2} + y^{2}) j$
C: The triangle bounded by y = 0, x = 3, and y = x

Dolly Robinson 2020-11-01

Find the following integral.
$\int \frac{x^{2} - 1}{x^{2}} d x$

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Calculus and Analysis