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Q: Use substitution to find the indefinite integral. Зх + 7 (6x + 28x) 5 3x +7 (6x² + 28x) =xp.

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Q: /12. É (sin *xcosx+ sin xcos.x) dx

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Q: Find V (V × F), if F(r, y, z) = 7e"i+6xe"j – 2ev²k. V· (V × F) =|0

A: We have to find ∇.∇×F→

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

A: Solution: C′(x)=3x2 −5x​; C(0)=2,000

Q: Find the indefinite integral. (Use C for the constant of integration.) 6 + 9x dx (x8 + 1)e*³.

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Q: Evaluate the integral / (4x + 12y)dx + (15x – y)dy along the parabolic arc y = x² from (0,0) to (1,…

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Q: a. Find the derivative function f' for the function f. b. Determine an equation of the line tangent…

A: Given : f(x)=7x+1   To Find : a) Derivative of f(x) b) Tangent at point (a,f(a)) where a=5

Q: Use Green's Theorem to evaluate the integral. Assume that the curve C'is oriented counterclockwise.…

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Q: Find the characteristic equation and eigenvalues of the matrix and a basis for each of the…

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Q: 2. A force of 5.0N is applied at the end of a lever that has a length of 2.0meters. If the force is…

A: We need to find the torque when we are given values of force  & length of liver and angle to the…

Q: Find div F and curl F if F(x, y, z) = 13y'2*i – 11x°z®j – 7xy°k. %3D div F= 0 curl F=|(-35 z y³ + 99…

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Q: The derivative with respect to x of (3i-1)ar is 3-1 by the 2nd fundamental theorem of Calculus A…

A: let f(x) =∫3x ( 3t-1) dt

Q: A spring with a natural length of 10 cm, is stretched by ½ cm by a 12 N force. Find the work done in…

A: Given query is to find the work done .

Q: 4. a = 20 m [W 30°S] b = 30 m [W 40°N]. Find a - b. %3D %3D

A: We need to find a-b.

Q: For the rational function f(x) = find the following limits and identify the type of asymptote that…

A: Given: Rational function: f(x)=4x-1x+9

Q: Consider a triangle ABC like the one below. Suppose that b= 33, a=48, and B 26°. (The figure is not…

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Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

A: We have to find maclaurian series

Q: Find div F and curl F if F(r, y, z) = 13y"2°i – 11a2°j – 7xy°k. div F= curl F=

A: We have to find the  divF and curl F

Q: 4- if U(x,y) = x2 + 2y and x(r, t) = r sint, y(r,t) = sin?t, au find 1- ar au and 2- at au 1- ar ди…

A: Given that,   U(x,y) = x2+2y   and x(r,t) = rsint,     y(r,t) =sin2t we have to find ∂u∂r,    ∂u∂t…

Q: is an improper integrat. dr A True B False

A: To check : The statement "∫-121x2dx is an improper integral." is True or False ?

Q: Find the eigenvalues of the matrix and determine whether there is a sufficient number to guarantee…

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Q: 2. sin 2wcos 2wcdw

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve Cis oriented counterclockwis p…

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Q: Find the unit tangent vector to the curve at the specified value of the parameter. r(t) = 5 cos(t)i…

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Q: PART III: APPLICATION 5. a and b have magnitudes of 5 and 6, respectively. The angle between them is…

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Q: Use the Fundamental Theorem of Calculus to find the "area under the curve" of f(x) = 8x + 7 %3D…

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Q: dx (x– 1)%

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Q: dr a 2 1 +3

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Q: Find the area of the surface generated by revolving the curve about each given anis. *- 7t. y= st,…

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Q: f(x) = x-5/x+8 find the domain

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Q: Use Lagrange multipliers to find the extreme values of the function f(x, y, z) = x² +y² + z2 subject…

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Q: Q2: You have the matrix How can we get the transpose matrix

A: Given problem:-

Q: Find an equation of the hyperbola having foci at (1, -7) and (1, 3) and vertices at (1, -5) and (1,…

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Q: The graph of the function f(x) = sin(x+ 8) is shown along with the points (– 8, f( – 8)) and (– 7,…

A: (1) f(x)=sin(x+8)f'(x)=cos(x+8)slope =f'(-8)=cos(0)=1equation of tangent at…

Q: Find the area of the quadrilateral lot shown in the figure below to the nearest square foot. 130 ft…

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Q: Use the function f and the given real number a to find (f -1)'(a). (Hint: See Example 5. If an…

A: Topic:- trigonometry and application of derivatives

Q: 2. sin 2wcos 2wchw

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Q: Sketch the region enclosed by y 6x and 4x. Find the area of the region.

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Q: Find y': y = ar csc(2a2)

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Q: Find the derivative of the function: y = (e**)e Oy = e (e*+ + 1) Oy - (e") (e*+* +1) Oy = (e…

A: We know that derivatives of  d(xn)/dx = nxn-1. And d(ex)/dx = ex.   Here i attached the solution of…

Q: You are given the following information about a termite colony population. The current population is…

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Q: Find V· (V × F) if F(x, y, z) = 9 sin xi + 5 cos(2x – 3y)j+ 7zk. - V·(V × F) %3D

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Q: Problem 8 Find the following indefinite integrals: (a) [3r°dr (b) S(3r® +9x² – 12r)dr (c) S(7x-1…

A: topic- indefinite integral ∫xndx=xn+1n+1+C

Q: You are given the following information about a termite colony population. The current population is…

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Q: Use the method of cylindrical shells to find the volume generated by rotating the region bounded by…

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Q: (b) Using the Power Rule for differentiation, find the derivatives for the following functions: (i)…

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Q: Calculate s f(x, y, z) dS for the given surface and function. D(r, 0) = (r cos(0), r sin(0), 0), 0<r…

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Q: Find V· (V × F), if F(x, y, z) = 3ei+ 4.xe®j – 2ev²k. V·(V × F) =

A: We need to find dot product.

Q: C. coordinate

A: answer is in next step

Q: Find the average value of the function f) = 8-7 on the interval [0, 9]. %3D

A: