dy Compute the derivative y dx y = 5x4 – x-4 (Express numbers in exact form. Use symbolic notation and fractions where needed.) 4 20x + y'

Q: Evaluate the integral / (2x + 6y)dx + (15x – y)dy a C arc y = x² from (0,0) to (1, 1). NOTE: Enter…

A:

Q: he curvature and the radius of curvature at the stated point. r(t) = 3 cos(t)i + 4 sin(t)j + tk; t 2…

A: Please refer to the image below

Q: an

A:

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

A:

Q: (-1)"2"x" n=1

A: We will use ratio test to find radius of convergence.

Q: Find the indefinite integral and check the result by differentiating. Determine an appropriate…

A: Solve the given intregal

Q: A forest fire is found at midnight. It covers 1100 acres then. It is spreading at a rate of f(t) =…

A:

Q: Find div F and curl F if F(x,y, z) = x*i – 7j + yzk. - div F= curl F=

A:

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

A: Improper integral: If f(x) is not continuous at x=c where a<c<b and ∫ac f(x) dx and ∫cb f(x)…

Q: Calculate x sin(y)dxdy

A: On solving this we will get

Q: Let I be the flux of G = (2e", 4x°e*“, 0) through the upper hemisphere S of the unit sphere. (a)…

A:

Q: Graph the eauation - include local+ Absolut extreme Points if applicable - -include inflection…

A: maxima minima

Q: ||r(t) × r"(t)|| Use the formula k(t) : to find «(t). %3D r(t) = e"i+e-tj K(t):

A: K(t)=?

Q: Match the vector field with its graph. F(x, y) = xi + 3yj 5- 5 -5+ -5+

A: Given data÷

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: Please help

A:

Q: The answer above is NOT correct. Use calculus to find the volume of a cap of a sphere with height h…

A:

Q: L (21 +x+3)dx

A:

Q: y 3 y = V x 1 (1, 1) X = 8 y = X 2 4 6 8

A:

Q: Find V × (V × F) if F(x, y, z) = 6xyj+ 4xyz k. V x (V × F

A:

Q: Find all relative extrema of the function. Use the Second-Derivative Test when applicable. (If an…

A:

Q: Find curl (2z i + 3x j + 6y k). curl(2z 2z i + 3x j+ 6y k) = ( i )i + ( i j + ( i )k

A:

Q: Approximate the point of intersection of the graphs of f and g. Then solve the equation f(x)=g(x)…

A: This question is related to Functions, we will solve it using given information.

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: 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: Show your work to determine the derivative of f(x) = (-1/x2 + 1/2 x2)(√x - 3x4). Do not simplify…

A:

Q: Find the average value of the function f(x,y)=eˆ(y/x) over the region bounded by y=x, the x-axis and…

A:

Q: A conical tank with a diameter of 2 m across the top and 3 m high is filled with water. Find the…

A: The given problem is solved below in detail.

Q: Evaluate the line integral / (3x + 9y)dx + (4x – 5y)dy along the curve C : x = 10 cos t, y = 20 sin…

A:

Q: 6. Find the indefinite integral. S 3x³ V3x4 + 7 dx (Use substitution method)

A: Solving the problem by finding the value of integration.

Q: 4. a) Find the average value of the function over the given interval. f(x) [4, 25] Vx'

A:

Q: п! n4 n=1

A: The given series is: ∑n=1∞n!n4 Let, an=n!n4; n≥1

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: у" — у' — бу %3D2, у (0) %3D 0, y'(0) = 0

A: Given can be written as (D2-D-6)y=2 The general solution will be y=CF+PI Complementary Factor(CF):…

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

A:

Q: Determine the derivative of f(x) = 2x2 - x3 using the first principles definition of the derivative.…

A: Given f(x)=2x2-x3we know that using first principles f'(x)=limh→0f(x+h)-f(x)hThen…

Q: dy Solye the differential equation 3a2y = = -y, s.t. y (0) :

A: Topic = Differential equation

Q: the

A: We will find the derivative.

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: Evaluate the line integral using Green's Theorem and check the answer by evaluating it directly. 3 y…

A:

Q: 2. Use the Divergence Theorem to compute ffs F. dS for F = (xy, yz, x² z + z² ) and S the boundary…

A:

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: For a plane curve r(t) = (x(t), y(t)), |æ'(t)y" (t) – x"(t)y' (t)| (x'(t)² + y' (t)²)³/2 - k(t) Use…

A: Here we have to use this equation to compute the curvature at the given point.

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

A:

Q: :. Let x(t) = 2 sinh t , y(t) = cosh(t²) be a curve in the Oxy-plane, given in parametric form. (a)…

A:

Q: sin(x) 19. Evaluate -dxdy by changing the limits of integration appropriately.

A:

Q: work shoWN. 1. Let v and w denote nonzero vectors. Show that the vector v- aw is orthogonal to w V.…

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: 21 The function f(x) is represented in the following table. Give the best estimate for f(x)dx 3 9.…

A: