In(v¤) dædy 6. 15. Calculate ry

Q: x+1 dx

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Q: [2.xyy' – y² +, Vy* +x* ; 4– %3D

A: ∫x2+a2 dx = xx2+a22+a22lnx+x2+a2+C

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

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Q: Find the derivative of this function

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Q: Consider the piecewise-defined function Jr+3, |1- x, x 0. (a) FUNCTION, so it must pass the…

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Q: Evaluate the following sum: 3x + cos 2016 + cos (Write your answer in the simplest form, use…

A: The given sum,1+cosπ3+cos2π3+cos3π3+cos4π3+......+cos2016π3

Q: 22. u = Vr² + s², r = y + x cos t, s=x + y sin t; ди ди ди əx’dy when x = 1, y = 2, t = 0 dt

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Q: A ball is launched straight up in the air from a height of 5 feet. Its velocity (feet/second) t…

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

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Q: Find V· (F × G), if F(x, y, z) = 8xi+j+8yk and G(x, y, z) = xi+ yj – zk. V · (F × G)

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Q: a) fx² sec2

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Q: 2. Compute Ja F · ds for F c(t) = (t , In(1+ t²), e*) for 0 <t < 1 VV, where V(r, y, z) = 4x² In(1+…

A: Find your answer below

Q: S%3200000 e° find the growth rate of S.

A: Given query is to find the growth rate.

Q: Evaluate (2x – y) dx + (x + 3y) dy. C: x-axis from x = 0 to x = 4

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Q: x – 1 - V3x +1 lim Зх + 1 x→5 X – 5

A: Solution:

Q: 4–6 Find the directional derivative of f at the given point in the direction indicated by the angle…

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Q: Find the volume of the region enclosed by z = 1 – y? and z = y² – 1 for 0 < x < 21. V =

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Q: cos x e) f(x)= e* х

A: Topic = Derivative

Q: Use Green's Theorem to evaluate the line integral. dx + (2 + x) dy -y2/2 - C: boundary of the region…

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Q: rocket weighs 2500 tons at liftoff and burns fuel at a rate of 12 tons/minute. Express the rockets…

A: Given query is to find the expression for rocket weight and time.

Q: 7. 1 (x dy – y dx) = 0 %3D x² + y²

A: Here, the given DE is: 1x2+y2(x dy -y dx)=0...(1)

Q: Evaluate the integral. (Use C for the constant of integration.) 2 cos (a) da sin(a)

A: Given query is to find the value of the integral.

Q: Question8: Choose one answer. You decide to collect a bunch of cans of soda and measure the volume…

A: To solve the following problem

Q: 5² - 13 ニ

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Q: Determine an equation for the tangent to the curve f(x) = 2x3 + 6x2 - 2  at x = -3

A: Given query is to find the equation of the tangent.

Q: Consider the function f(x): - 4x + 6x - 8. f(x) has a critical point at x A. Find the value of A: A…

A: For critical points ofa function we first find the derivative of the function and equate it to zero.

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

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Q: Consider the matrixes 0 3 -9 k A = O .B = ( , 7 7 62 k is a real constant M = (A-B-1)-1 If m22 = 14…

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Q: Q1: Find partial derivatives of the function with respect with each variable 3) f(x, y) = (xy – 1)}…

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Q: 2X メ→チ 7-x

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Q: Let be A, B, C,x. 5x5 matrixes such that A, B and C can be inverted such that AXB" – 151, = c-1…

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Q: Find the length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: Find the curvature and the radius of curvature at the stated point. r(t) = 7 cos(t)i + 3 sin(t)j+…

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Q: Find the vector 2u +3w given the vectors u =-i-4j and w = -2i + 5j. Write your answer in the form a…

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Q: Use the first principles delta method to find the derivative of y = x2 – x. %3D

A: Here we have to find the derivative of y by using the first principles delta method.

Q: 2. True or False? a) -2(3BA)and 6AB'are equal vectors. Justify your answer. b) If |AB| = |AC|, then…

A: This question can be solved using the concept of equal vectors.

Q: Mic differentiation to Find der :Vative Of Y «in(x+7) x+7)* (In(x+7) + X. X-1 H7)* (x+7) t x+7

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Q: 3+ 12x4 – 7x +x³ a) lim 2л2 — За3 + х — 424 3x3 +x – 4x4* - -

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Q: Find the directional derivative of f(r,y, z) = e² cos(Tyz) at (0, 1, ) in 2-1 -y-1= I-2 the…

A: To Find: Directional derivative

Q: 1. Sketch a single graph of a function f(x) which satisfies all of the following the limits and…

A: The function satisfies,f-3=1, limx→-4f(x)=-1, limx→2-f(x)=-∞, limx→2+f(x)=∞, f'(4)=0f(2)=2,…

Q: Evaluate the improper integral |. 3.x dx or show that it diverges. +1 x?

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Q: Apply the Ratio Test to each series to determine whether the series converges, or state that the…

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Q: Use the One-to-One Property to solve the equation for x. 3x - 1 = 27 %3D X =

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Q: e-2x 2+x In 3x csc' x -) f(x)=. b)Use logarithm to differentiate: y = (3х-1)

A: a)f(x)=ln(3x)csc2x-x5e-x3f(x)=sin2x. ln(3x)-x5e-x3differentiating w.r.t…

Q: 2Tan 'x - x 9. lim,0 'x0 2x – Sin 'x

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Q: Consider the parametric equations below. Assume that t can be any real number. x=t-3, y=2t-5…

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Q: 1. E(n + -3 2 n=1

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Q: 23. y²dx + (xy – 1)dy = 0

A: Let's find.

Q: Find dy/de y=(1 +Sin 94)6

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

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