Find div F and curl F if F(x, y, z) = 13y°2°i – 13x³z1°j – 5xy'k. ,5 „10; 6 „6: - div F= curl F=

Q: Find the value of the following definite integrals. Show your solution. 1. L* + 4) dx 2. f(cos x +…

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Q: The length of the curve determined by equations x = 8 cos t + 8t sin t and y = 8 sin t – 8t cos t…

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A: Given : f(x)=xx2+1   To Show: f'(x)=1-x22x(x2+1)3

Q: Problem 3: Given a function 4 - x2 g(x) = 3 - Vx2 + 5 Page 1 of 3 Use analytical method to determine…

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A: Use substitution method for solving the  integral.

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Q: Find curl (8z i + 9x j + 8y k). curl(8z i+ 9x j + 8y k) = ( i )i + ( i j + ( )k

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Q: 6. Given f(x,y) = x² – 2xy² – 4xy + 5. Find all the critical points of f and determine the nature of…

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Q: Evaluate sin? xcos xdx .

A: To evaluate: ∫sin2x cos3x dx=∫sin2x cos2x cos x dx=∫sin2x (1-sin2x) cos x dx

Q: xp - )s ɛ

A: As per the guidelines I can solve only first question

Q: 11. Let -4 А -4 -4 -3 -3 (a) (i) Show that -4 is an eigenvalue of A with corresponding eigenvector…

A: As you have asked multiple subparts so I have answered first three subparts as per the guidelines.

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A: Solving

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Q: Determine the open Intervals on which the graph ts concave upward or concave downward. (Enter your…

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Q: Find the limit of the following sequence or determine that the sequence diverges. 15 Select the…

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Q: (8x + 4x)v4x² + 8 – 24x³ – 32x If f(x) = (/4x2 + 8 - x*) then f'(x) = 4r2 +8

A: f(x) = (4x2 +8 - x2 )2 f'(x) = (24x2 +8 - 2x2)(8x/(24x2 +8)  -2x ) f'(x) = ((24x2 +8 - 2x2)(4x -…

Q: dzy What is dx2 for the curve given by x = t2 and y = t3?

A: Our Aim is to find d2ydx2 for the curve given by x=t2 and y=t3

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Q: Зx* у + tan y dy Given a first order differential equation dx x³ +x sec? y (a) Clarify the exactness…

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Q: Problem 3: Given a function 4 - x2 g(x) = 3 - Vx2 + 5 Page 1 of 3 Use analytical method to determine…

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Q: Q2) Find the integral of: f*,6 tan*x dx

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Q: Consider the exact first order diff. equ: M(x, y) = 2.xy – 3x² N(x, y) = x² – 2y (I): (2xy-3x )dx +…

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Q: A. Use polar coordinates to describe the region shown. 1.

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Q: Factor the expression. Use the fundamental identities to simplify, if necessary. (There is more than…

A: Given problem:- Factor the expression 1-2cos2(x)+cos4(x)

Q: ||r(t) × r"(t)|| ||r(t)||³ Use the formula k(t) = to find k(t). r(t) = 4 cos(7t)i + 4 sin(7t)j + 3tk…

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Q: x² Consider the function f(x) = x² –1 (a) Find the intercepts of the graph of f (if any). (b) Find…

A: This is a problem related to function calculation. Based on the general formula and concept we will…

Q: dy cos (x) cos (Y) %3D da O a. 2 In sec (3) +tan (3)| = %3D O b. 4 In sec (3)) + tan (y) %3D

A: Given: dydx=cos2x cosy

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Q: Find r'(t). r(t) = (tan-(7t))i+t cos(t)j – Vēk

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Q: Consider h(x, Y, z) = cos (xy) + eY% + ln (xz). Determine the directional derivative of h at the…

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Q: 7. Find the linear approximation near (2, 0) of f(x, y) = 3x e¯3ªy.

A: To find the linear approximation for the given function.

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Q: ||r'(t) × r"(t)|| Use the formula k(t) : to find k(t). ||r'(t)||* r(t) = t’i + t®j 390 t14 K(t) = t3…

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Q: Find the differential dy: y = sin(av). dy = " cos (av) [2v + a+i In a (1 + Ina p + x!+ In ¤ (1+ ln…

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Q: Find r'(t). r(t) = (tan-(11t))i+t cos(t)j – Vtk | NOTE: Enter your answer in terms of i, j, and k.…

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Q: 7. Interpretations of Inter a) Determine the position function, s(t), of an object if the…

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Q: Find V x (V x F) if F(x, y, z) = 2:xy j+ 9xyz k. V x (V × F)

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Q: Find curl (8z i + 9x j+ 10y k). curl (8z i + 9x j+ 10y k) (i )i + ( i j + ( )k

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Q: Suppose that f(r, y) ry. The directional derivative of f(x, y) in the directional (1, - 1) and at…

A: directional derivative f(x,y) = adf/dx +bdf/dy (a,b) = (1,-1) df/dx = y df/dy = x directional…

Q: Find div F and curl F if F(x, y, z) = x*i – 11j + yzk. div F= curl F=

A: Vector

Q: Find r'(t). r(t) = (tan¬(11t))i+t cos(t)j – vtk NOTE: Enter your answer in terms of i, j, and k.…

A: Here, the given vector function is: r(t)=(tan-1(11t))i+tcos(t)j-tk

Q: Find the volume of the solid Formed by revolving the region bounded by the graphs OF y=x +1, y = 0,…

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Q: Let T6 (x): be the Taylor polynomial of degree 6 of the function f(x) = cos(x) at a = 0. Suppose you…

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Q: Use the formula k(t) = |r(t) × r"(t)|| ||r(t)||° to find «(t). r(t) = 8 cos(7t)i+ 8 sin(7t)j + 3tk…

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Q: Find [r(t) · u(t)] and [r(t) × u(t)] in two different ways. dt dt r(t) = ti + 8t2j + t³k, _u(t) =…

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Q: Q5) Find the integration by using (by part method): Se3x sin X dX

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