Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j and k. (a) Same direction as 3i + 8j. - и — (b) Oppositely directed to 12i – 8j + 8k. v = (c) Same direction as the vector from the point A(-1,0,4) to the point В(4, 3, 3). W =

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A: Given query is to find the derivative if the expression.

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A: We know sequence is convergent when limit of sequence is finite

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A: The objective is to solve the above question. 

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A: see below the answer and figure

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A: Solved below

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Q: S sin(1 – x) (2 – cos(1 – x))* dx A (2-sin(1-x)5 (2-sin(1-x)5 +C +C D (2-cos(1–x)5 +C (2-cos(1–x)5 +...

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A: Given,             ∫x2-1xdx

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A: Let's find. 

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A: We will find the derivatives of the given function y=ecos2x in the following step.

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A: The given differential equation is : y"'-5y''-6y'=3e2x. Repost the next part. 

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A: The objective is to find the total area.

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A: Since you have asked multiple questions in a single request we would be answering only the first que...

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Q: Find f"(x). If f (x) %3D 3x3 — Зx2 + х + 1 3x3 - 3x2 + x + 1 А) 3х- 4 (в) 9х- 6 (с) 18х - 6 D 6x -5

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Q: Exercise 1 In each of the following, use Lagrange multipliers to find the critical points and the re...

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Q: Using integration by parts, the integral 2 f cot-1 x dx equals: 2 x cot-1x+ In|x² + 1| + C - x cot-1...

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Q: Using Reciprocal Substitution * For S Option 1 Option 2 - (1 - 4t) + c

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A: By the ruler postulate: PQ = |y-x| QR= |z-y| PR = |z-x|. But y-x is positive because x &lt; y; sim...

Q: Exercise 1 In each of the following, use Lagrange multipliers to find the critical points and the re...

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Q: 1. What is the slope of the line tangent to the curve y=x3(x2-3) at x=-1? A. 1/4      B. -1/4      ...

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Q: For S dx, x = 1+ Vx O x = u^4 O x = u^(1/4) x = u None of the choices ООО О

A: We use those substitution which makes integral easy. Hence, x=u4 This is the required substitution.

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A: Given: I=∫35xdxx2-5   ....(1)   We know that; The logarithmic rule; 1). logaxb=b·logax 2). logbmn=lo...

Q: Evaluate the integral and check your answer by differentiating. NOTE: Enter the exact answer. |(7+) ...

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A: Since you have asked multiple questions in a single request we would be answering only the first que...

Q: 4. f(x)= 2x - 24.x 5. f(x) = 3x 3 -9 6. f(x) = 4x³ +12x? -96x

A: Let's find. 

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A: Given

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A: Given

Q: on the right. Prompts Submitted Answers D Ssin(3x)sin(4x)dx S(cos(x) - cos(7x)dx} Jsin(3x)cos(4x)dx ...

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Q: 2udu = 3 u? – (u²)?

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Q: Consider the parallelepiped with adjacent edges u = 9i + 6j + k v = i+j+7k w = i+ 6j + 6k Find the v...

A: The given equations are,  u=9i+6j+k v=i+j+7k w=i+6j+6k.

Q: Find the total area enclosed between y = x and y = x over the interval [-1, 8]. NOTE: Enter the exac...

A: This question is based on application of integration.

Q: Question 5 x3+5 Determine f '(x). f (x) = (A 1- 10x-3 B 3x2 3 2 (D 5x4 + 10x 2.

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A: Given problem:- ∫ [1+ sin2(θ) csc(θ)] dθ 

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A: This question is based on chain rule differentiation.

Q: 17. If y = tx, where t is the parameter, what are the parametric equations of the curve x' + y' = 8?...

A: solution:-y=txx3+y3=8x3+tx3=8x31+t3=8x3=81+t3x=21+t33

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated axi...

A: Given query is to find the volume of the solid generated.