e" dx 7.3. J- 1-e 2x

Q: Solve the initial value problem. d²y = 2 e -X, y(0) = 0, y'(0) = 4 dx

A: ∫ d2ydx2 =∫ 2 e-x dxdydx=2e-x(-1)+Bdydx=-2e-x+B ...(1)

Q: what is (x fyx+ fy) given fCKiy)= ey

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Q: A ball bearing is placed on an inclined plane and begins to roll. The angle of elevation of the plan...

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Q: The exponential model A = 676.7 e0.031 describes the population, A, of a country in millions, t year...

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Q: Given the function f(x) = (x+3)²(x-1). Find the critical points of f(x) and its increasing and decre...

A: f(x)=x+32x-1f'x=x+32ddxx-1+x-1ddxx+32       =x+32+2x-1x+3       =x+3x+3+2x-1      =x+33x+1to find cr...

Q: Evaluate the derivative. 6) f(x) = csch¬1(6/x)

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Q: function f(x) is given.  f(x)=log2 (log5 (x)) a)find the domain of the function f. (enter your ans...

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Q: Given the the parametric curve S x(t) = est – 2t l y(t) - 8t sin t dy (a) Find an expression for dx ...

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Q: Consider dx and using u-substitution in rewriting the integrand as a function of u and du. Determine...

A: For the solution follow the next step.

Q: Problem 4. Find all real zeros of P(x) = 3x-5x'-16x +7x+15 using the techniques we discussed in clas...

A: We solve this question with the help Rational root test.

Q: Evaluate Log base (1-i) (1+(sqrt of 3)i) and express the final answer in polar form.

A: Given: - log(1-i)(1+3i) To evaluate: - The final answer in polar form.

Q: Solve the initial value problem. ds 281(7? – 5)°, dt s(1) = 12 4 (71² – 5) + 4 The solution is s = 2

A: This is a problem of integration. By using below formula we will calculate integral and then will su...

Q: A differentiable function f has one critical number at x = 8. Identify the relative extrema of fat t...

A: We have to choose correct option

Q: Find the midpoint of the line segment with the given endpoints (-7,- 1)and (- 3,- 2) The midpoint is...

A: The midpoint of the line segment with the endpoints (x1,y1) & (x2,y2)is given by: x1+x22,y1+y22 

Q: 2. Show your solution. The sample space that describes all three-child families according to the gen...

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Q: Find the derivative of f(x) = sec(tan(x) + cot(x))

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Q: emine whether the series is convegent or divergent. If it an=lo00,evaluate lim Can) Cos M8

A: We have to find the value of the given limit according to the given information

Q: Graph both the parent function and f (r) on the same coordinate system, labeling at least three poin...

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Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

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Q: (16) cos (xy) find dy/dx

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Q: Evaluate O a. 2/ + 3+ 3-6ln |z/+1|+C O b. 2 3T+ 32 +6ln r/ +1+C O c. 2vE - 3T +322 – 6ln |z'/0 – 1|+...

A: ∫1x+x3dx

Q: Solve using the U-Technique Question 17 For f (-4х-12) dx (x+10)³(x-4)³ F(x) - 1. What is F(3)? ... ...

A: given that ∫-4x-12x+103x-43=Fx-1find F3

Q: Find the indefinite integral. (Use C for the constant of integration.) sin x dx 3 + cos² x

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Q: " + y = 12 cos 2x - sin x. A. " + y = sin 3x +4 cos x. A

A: Given: y''+y=12cos2x-sinx

Q: Find all the second-order partial derivatives of the following function. h(x,y) — хеУ + 8у +4 %3D dx...

A: Solution :hx,y=xey+8y+4∂h∂x=ey∂h∂y=xey+8∂2h∂x2=∂∂x∂h∂x=∂∂xey=0∂2h∂y2=∂∂y∂h∂y=∂∂yxey+8=xey

Q: der the following function. (x) = 9 - |x - 1| (a) Find the critical numbers of f. (Enter your answer...

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Q: Convert the parametric equations of a curve into rectangular form. No sketch is necessary. x = 3t + ...

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Q: A Plane flies 320km due West and then 240km due North. W- ►E 320 km 240 km

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Q: The graph of y3f(x) is given. Solve the inequalities. Write the solution sets in interval notation i...

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Q: Find the surface integral F. dS of the vector field F(x, y, z) = (-x, -4, yz®) along the part of the...

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Q: Determine Functions Directions: Determine which relations represent a function and then drag each in...

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Q: Given f (x) = 1- 1 / (x + 2)² Find : f(-x)

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Q: Find the sum of the series: п (п - 3) n=5 or conclude that it diverges. A) 0. 11 B) 3. 13 C) D) E) D...

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Q: Consider the following function. (x) = 3x3 + 9x2 – 27x (a) Find the critical numbers of f. (Enter yo...

A: Consider the function f(x)=3x3+9x2-27x, then we have to answer the following... Solution (a): To fin...

Q: Convert the parametric equations of a curve into rectangular form. No sketch is necessary. x = Vt, y...

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Q: Classify the series as absolutely convergent, conditionally convergent, or divergent. k Σ 2ln k k=2 ...

A: We know about conditionally convergent when series absolutely divergent.

Q: solve for x the equation 4y 3x2 + 2r - 5

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Q: Let A= [a, b c, d, e) and B=(a, b, c, d, e f g, h). Match the given sets in the left to the sets in ...

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Q: By applying integration by parts, we have Jx° In x dx = x10 In x +10 + C 10 100

A: given :   integration by parts 

Q: Find the point on the curve y = 23/2 for which the tangent line to the curve is perpendicular to the...

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Q: Compute dy/dx for the function. 5) y = In sinh 6x

A: topic- derivative of a function

Q: Determine whether the series converges. Σ k=1 V8k – 1 The series converges. O The series diverges.

A: To determine: The convergence of ∑k=1∞ 18k-13.

Q: Given the following table of values, find h' (-1) if h(x) = (x* + p(x))". -1 1 p(x) -2 1 p'(x) 2 3 -...

A: Necessary  formula: The derivative of   xn   is   nx(n−1)

Q: Find the Maclaurin series for the func f(x) = cos 2x %3D f(x) = %3D n=D0

A: given:f(x)=cos2x

Q: mpany has a cost for producing x items of 55x+33 and revenue is 95x-0.5x2 what is the profit

A:   The profit is the revenue minus the cost

Q: Evaluating Definite Integrals Use the results of Equations (2) and (4) to evaluate the integrals in ...

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Q: xp 7.1. 4x²-4x+5

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Q: th 1. The 6 term of an A.P. is -5 and the 10" term is -21. Find (i) the 8th term (ii) the sum of the...

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Q: dx Vx + x

A: topic - integration 

Q: tan' sec? 그dr 26. 28. 7 dr - 10

A: