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 + 7j. u =

Q: Find the following. a. da Pro b. da le 4] = %3D C. dr (5e 02] = %3D

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Q: let z- 57 dy .. dy By chain Ruie

A: The objective is to find the second derivative using chain rule.

Q: Let a = (2, –3, 5) and b = (4, 1, –1). Compute: a +b = (. a – b = ( 4. 2а 3

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Q: - (2e'cos t) i+ (2e'sin t)j 7K Find T, N, and k for the space curve 7k.

A: Given,           The space curve is rt=2etcosti+2etsintj+7k.To find : Find, T, N and k for the given...

Q: Fg(x) = 1 Vx-1

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Q: Evaluate the double integral. (2x + y) dA, D = {(x, y) | 1 s y s 2, y – 1sx s 1} 328 3.

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Q: The sum of a geometric series is as follows: S = 1.0 + 1.1 + 1.21 + 1.331 +... up to 50th term. Dete...

A: SUM OF GEOMETRIC SERIES

Q: 3. At midnight, the heater inside your house breaks down. The temperature (T) inside your house at t...

A: dTdt=-k(T-T0)∫ dT(T-T0)=∫-k dtln(T-T0) =-kt+ln CT=T0 +C e-ktat t=0;T(0)=21°CT0 =-6°C21=-6+CC=27T=T0 ...

Q: Find the derivative of g(x) =

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Q: + 2y = 7x +4; y(0) = 3, y'(0) is y(x) =. %3D

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Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and...

A: Given   xy=4

Q: 1. Use the e - d definition of the limit to show the following: (a) lim(5x – 2) = 3 エ→1 (b) lim Vr =...

A: The objective is to use definition of limit to prove the above question.

Q: 2. f (x) - 2x2 if メくQ 2- メ if x 2 2

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Q: Solve the following initial value problem. y"-2y'+ 2y 7x +4; y(0) = 3, y'(0) =0 The solution is y(x)...

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Q: Find the points on the graph of z = xy + 8y-1 where the tangent plane is parallel to 6x + 5y + 6z = ...

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Q: DO NOT include spaces in between 17 characters. * Compute m d (In (In y)) at y=e. dy Your answer

A: The objective is to compute the derivative at y=e.

Q: 3.4 +3.198

A: Consider   

Q: Find the angle between two vectors by using cross product (V,xV2) V, = 3i + 9j + 6k V2 = i + 3j + 2k...

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Q: Find the general solution of the differential equation. 55y4) + 49y" + 4y= 0 y(x) =D %3D

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Q: 2 NOT: L..

A: We have to find the value of x such that f(x)bis continuous but not differentiable

Q: DO NOT include spaces in between characters. * Find f' (-;) if f(x)= 3. Your answer

A: The objective is to find the derivative  of f at (-2/3).

Q: Calculate the volume of the solid formed when the area shown below enclosed by the curve y = Vx, the...

A: To find the volume of the region bounded by the curve y=x, x=0, x=6:

Q: Find the volume of the solid enclosed by the paraboloid z = 4 + x2 + (y – 2)2 and the planes z = 1, ...

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Q: 9. given f(-2) = 5, f'(-2) = -3, g'(-2) = 6, f g)'(-2) = 15. Find g(-2) %3D

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the exact answers using the provide...

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Q: 1. Calculate the area enclosed by the line y 2x + 3, the x-axis, and the lines x 1 and x- 3.

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Q: Suppose that the functions f and g and their derivatives with respect to x have the following values...

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Q: Write an equivalent first-order differential equation and initial condition for y. y= -1+ ](5t - 3y(...

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Q: Use the position function s(t) = -16t2 + vt + s, for free-falling objects. %3D A ball is thrown stra...

A: keeping a note ?as per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Ki...

Q: 4x (log3 x)° (csc5 x) Vsinh(2x – 8) b. y= -

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Q: Q3/B/ Find the value of unknown in the following 1 -2 7 9 5 6 ? 3 ? -2 7 1 6 1 -2 7 +4 ? 1 - 5 6 -3 ...

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Q: Evaluate the integrals that converge 32 1 dx 2 ㅇ x5

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Find f'(x), if: f(x) = (x-2/2x+1)^9

A: Find your answer below 

Q: = cx + In(cos x). For what value of c is f'(T/4) = 7? C =

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Q: 2x2-8х+7 x 0 9x2+5x-3' Suppose f (x) = -4х3 +6х2—15 х-6х3

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Q: O g(x )= ( % x + %); X so , at the point X,=O. x >0 9x - X

A: To check the continuity, we will see the limit of the function at x=0  and the function value at x=0...

Q: Instructions for forms of answers in differential equation problems: For second order DEs, the roots...

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Q: d Compute [(* + 2x)} ] a x= -1. dx

A: ddxx5+2x2=2x5+2x5x4+2

Q: x? + y? = = 169 (a) Find dy/dt, given x = 5, y = 12, and dx/dt = 7. dy/dt = (b) Find dx/dt, given x ...

A: We will find the derivatives and value at a point. 

Q: Find the exact value of the expression. cos(160°) cos(25°) + sin(160°) sin(25°)

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Q: y"-8y'+2y xe

A: Answer of given question is in step2

Q: DO NOT include the variable in your answer. Given the graph off'(x) below, what is the slope of the ...

A:

Q: O Evalunte

A: We will evaluate the double integral. 

Q: %3D 32 5. Let g be a differentiable function such that g(4) = 5 and g'(4) = -2. If the tangent line ...

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Q: 4. Find the volume of the solid obtained by rotating the region bounded by y = e", y = 0, x = -1, x ...

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Q: The sequence that begins , -2, , -5, , .. -13 could be . an alternating sequence. a harmonic sequenc...

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Q: 10. The line y = 5x – 5 is tangent to the graph of f (x) = (x + k)(x² – x) at the point where x = 1....

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Q: For each of the following y, find the d^2y/dx^2

A: We know, d/dx (xn)= nxn-1, for any real number n. d/dx(u(x)v(x))= v(x)*d/dx(u(x))+u(x)*d/dx(v(x))

Q: lim(32x-3 + 5) X4

A: The given limit,        limx→432x-3+5

Q: Pollution levels in a lake have been modeled by the equation x = 0.09 + 0.16e-0.38t where x is the v...

A: