Find the directional derivative of the function at P in the direction of v. f(x, y) = x3 - y³, P(4, 3), v = _ (i + j) %3D

Q: Find the volume of the solid obtained by rotating the region in the first quadrant bounded by the…

A:

Q: Evaluate the line integral / -ydx + xdy along the curve C C : y? = 27x from (27, 27) to (0,0). NOTE:…

A:

Q: r'y'y'+ xy' = 1

A:

Q: nd the S (1–) dx A. x– 2 In|x| – +c B. 3x – 2 In|x| –-÷+c C. 2x – In|x| –+c D. x– In|x| - +c

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 7. Determine the following general antiderivatives. cos (x) dx -dx sin(x) а. - b. 10 sin(x)cos(x) dx…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Determine the equation of the tangent to the graph of the equation xy – 2x'y-3ry + 5y – 4 = 0 at the…

A: To find the equation of tangent to the given equation at (1,2).

Q: ind lim f(x) for the given piecewise function. x-4 2х + 5 if x 4 E the limit does not exist, enter…

A: Topic  = Limits

Q: ||r'(t) x r' r"(t)|| Use the formula k(t) to find k(t). 3 ||r(t)||* r(t) = t'i+ t5j K(t) =

A:

Q: 2. A rocket is launched in the air. Its height (in meters above sea level) as a function of time t…

A: To solve the following problem

Q: Find the particular antiderivative of the following derivative that satisfies the given condition.…

A: I have stated the used formula in the solution

Q: Evaluate the definite integral. 9ti + 3t°j + Vtk) dt

A: The given definite integral,    ∫-119t i+3t3j+t3kdt

Q: Find V. (V × F), if F(x, y, z) = e²i+ 3xe"j – 7ev*k. - V · (V × F)

A:

Q: Determine whether the improper integral converges or diverges. Evaluate the integral if it…

A:

Q: E(-1)n+1_2 Vn n=1

A:

Q: For each sign chart for f. Carefully sketch the graph of both functions f and f. Upload your work as…

A: When derivative of f is positive then f is Increasing and when f' is negative f is Decreasing

Q: The function ƒ (x) = |x| is continuous at every real number. %3D False True

A: Let's find.

Q: Solve the system of differential equations. [ 3 x' 0 - 4. x1(0) = – 12, x2(0) = – 10 - æ1(t) = %3D…

A:

Q: Find the Laplace Transform of the following functions: a. L(sinxcosxe*} b. L{

A:

Q: d y Find dx? for the parametric equation: x = et;y3Dt³ +t+1

A: Find your answer below

Q: Calculate the area of the region bounded by the graphs of the given equations. x 2y2- 4, x = y2 + 5…

A:

Q: As you will show, exponential growth functions ekx always dominate power functions x", and power…

A:

Q: 1. Do the integration by substitution for the following integral and find the value of definite…

A: We have to find the given integral value.

Q: Find the derivative of the following function by applying the appropriate derivative rules. f(x) =…

A:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (e2i + Sin(/e) j+e-k 7t

A: Limt-0 (e2ti+sin(7t)j/(7t) +e-5tk).

Q: O A) B) 8 C) n O D) T

A: Given; y=√2 x

Q: Compute f(x)dx f(x) = { 2x if x <1 4 if x 21

A:

Q: For the given position vectors r(t), compute the (tangent) velocity vector r'(t) for the given value…

A: Find derivative of position vector then we get velocity vector then put the given value

Q: (

A: We will find the centroid of the triangle.

Q: Evaluate the indefinite integral: .3 dx x² – 2x + 5

A:

Q: b) S X sin xdx 0.

A: Integral by parts:∫uv dx =u∫vdx -∫dudx ∫vdx dxu=xv=sin x∫ vdx =∫sinx dx = -cos x+Cdudx=ddx(x)=1

Q: im Y cosx tZx 7x¢ with squeze thearem

A:

Q: Find div F and curl F if F(x, y, z) = 3e*"i – cos yj+ 7sin? z k. %3D div F= curl F=

A:

Q: Evaluate the iterated integral: x + 4y dx dy Answer :

A: We can solve as follows

Q: Find the 22 term of the arithmetic sequence whose common difference is d=4 and whose first term is…

A:

Q: The population P (in thousands) of Tallahassee, Florida, from 2000 through 2018 can be modeled by P…

A:

Q: y x = y - 2 y = 1 x = e -3 -1 1 2 4 | y = -1 3. 3.

A:

Q: 6) Find the SVD of the matrix by manually calculating U 4 11 14 A = 8 7 -2]

A:

Q: S (In 2x2 dx

A: Evaluate the integral :    ∫ln 2x2 dx

Q: 10 Find div F and curl F if F(x, y, z) = xz°i+ 5y"x²j+ 4z?yk. div F= curl F=

A: Solution:

Q: Use the shell method to find the volume of the solid generated by revolving the shaded region about…

A:

Q: Find the curvature of the plane curve y = -t at the point t = 2. к(2) -

A: Given:y = -t4differentiating with respect to t, we get:            y' =     d(-t4)dt…

Q: Inx Evaluate the limit using L'Hospital's rule: Lima0 cosh

A:

Q: Use the graph of the function f to decide whether the value of the given quantity exists. (If an…

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others part as…

Q: Describe the graph of the equation. r= 5 cos t i - 18 sin 1 j +k O An ellipse in the planex = 1,…

A:

Q: Find f. (x+ 1) (b) f'(x) = f(1) = 5 3.

A:

Q: A. Sketch the figure for analysis. Shade the needed region and draw a representative vertical or…

A: Here, the region is bounded by the curves: x=4, y2=x

Q: Use a double integral to find the volume of the indicated solid. 4아 2 30 z = 25 - xy 20 10 3. 2 y=x…

A:

Q: Find these derivatives

A: Our Aim is to find the derivative of the following functions given below:-(i) y=e2x cos (x)(ii) y=ln…

Q: Consider the functions. f(u) = u³ + u g(x) = cos (x) Find the following function and derivatives.…

A: The given functions,fu=u8+ug(x)=cos(x)

Q: If x + 1 f(x) then find the global minimum of f on the interval [1, c∞)

A: Given; f(x)=x^2+1/x