15. Challenge Problem: Find the value of k for which the following limit exists. 4x2 + kx - 27 lim x-3 2x2-5x - 3

Q: 1. Create a Table of Values to find the limit of each function. (Use at least 3 distinct values of x...

A: As per our guidelines, we can answer only one question in a single request. Kindly re-post the other...

Q: Suppose you deposit $7000 at 6% interest compounded continously. Find the average value of your acco...

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Q: Find the sum of the scrics k – Vk2 – 1 Vk(k + 1) - k=2

A: we will find the sum using sequence of partial sums. 

Q: IV. Find the equation of a line passing through (-1,4) and perpendicular to the line x+5y-4=0. V. Fi...

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Q: (3 Let f(x) = 2x2 01 waluate limits and continuity of f(x) at 1 and at 0.

A: The given function is f(x)=3x≤02x20<x<12xx>1  and f(1) is undefined. Here we have to evalua...

Q: e solution of the following Differential Equations 2) y"-16y 0 4) y"-y'-6y=0 6) y" - 2y' + 2y = 0

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Q: Let y=(x+sin(x))^5 Find g(x) and f(x) so that y=(f∘g)(x), and compute the derivative using the Chai...

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Q: solve the equation. (round your answers to four decimal places.) e^2x-8e^x +7=0 x=       (smaller ...

A: topic  - expomemtial equation

Q: Determine if each formula is right or wrong. Give a brief reason for each answer. Sax+27 dx= (4x+2)3...

A: The formulas are given by To determine: Whether the formulas are right or wrong with the brief reas...

Q: Since both equations will always be equal to zero, we will automatically move the V2 term to the rig...

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Q: Consider the indefinite integral *7x³ + 9x² + 12x + 24 -dx x4 + 4x2

A: Given,            ∫7x3+9x2+12x+24x4+4x2To find : The partial fractions decomposition.

Q: What is the slope-intercept form of the equation of the tangent line to y=x²+2x at x=0?

A: At x = 0, y = 0+0 =0  So, the tangent line passes through (0,0) .

Q: (sin x+ cos x). Find xp

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Q: Use the change-of-base formula and a calculator to approximate the given logarithm. Round to 4 decim...

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Q: I. Use the limit of the rates as Ax approaches zero. Ax 3. y = x3

A: Given: - y=x3, the limit of rates ∆y∆x as ∆x approaches zero. To calculate: - The complete solution ...

Q: Given F(2) = 4, F'(2) = 2, F(4) = 2, F'(4) = 7 and G(2) = 4, G' (2) = 1, G(4) = 1, G' (4) = 2, find ...

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Q: Consider the following. 2 + y- 16 (a) Find two explicit functions by solving the equation for y in t...

A: The objective is to solve the above questions. 

Q: Let the region R be the area enclosed the function f (x) = 3x3, the horizontal line y = 6, and the y...

A: Given:-the region bounded byf(x)=3x13y=6 and the y-axisrevolving about the line y=6using washer/disk...

Q: Part 1 of 2 Suppose f andfare differentiable functions. Suppose f(-8) - 9 and f'(-8) = - 4. %3D Ques...

A: topic - functions and derivatives

Q: 12) y"-3y' +2y=0, y(0) =-1, y'(0) = 0

A: topic - differential equations

Q: Determine the value(s) of k such that the system of linear equations has the indicated number of sol...

A: For infinite many solution ,  a1/a2 = b1/b2 = c1/c2   

Q: z(z² – 1) -dz z2 + 1 1 ²-In(z² + 1) + C A B z² + In(z² + 1) + C 글(22+ 1)2+C (D) z² + (z² +

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Q: (b) Write the function from part (a) as an exponential function of the form y=ae". Round b to four d...

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Q: Find the slope of the tangent line to the graph at the given point. (x² + 4)y = 8, (-2, 1) Witch of ...

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Q: Determine whether the integral is convergent or divergent. If it is convergent, evaluate it. (If the...

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Q: The following function is a company's price function, where p is the price (in dollars) at which qua...

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Q: 14) 4y" +4y'+ y 0

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as ...

Q: Determine whether the integral is divergent or convergent. If it is convergent, evaluate it. If not,...

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Q: For each function, determine whether it is a polynomial function. Is the function a polynomial? Func...

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Q: t11 +1 s(t) = t11 – 1 s'(t) =

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Q: Given the functions f(x) = 3+ Vã, g(x) = x² – 3, h(x) 1 - x m(r): I - 3 find the following: 3x + 5' ...

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Q: Given the matrix and its eigenvalues -12 has eigenvalues R, = -1 and R, 1 -5 = - 2 %3D Find the new ...

A: We have to find Matrix A1 and A2

Q: Given the following multiplication problem Equation 1: - 24V,=-8V2 -24 8 gives us equations -2 Equat...

A: From the matrix, we have the eigenvalues as  λ1=-26λ2=0 When, λ1=-26 the eigenvector is μ1=-41

Q: Given the following multiplication problem -2 1 = - 1 Perform the multiplication to find your two eq...

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Q: Consider the function f(z) = 4 8z on the interval [- 1, 4]. Find the average or mean slope of the fu...

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Q: A 5 m pole, Teaning against a wall slips in such a way that its base is vedin HOVing away from the w...

A: Draw the diagram and use the Pythagoras theoram and concept of rate of change. 

Q: Determine whether the improper integral diverges or converges. dx

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Q: coth? (x) – csch2(x) = 1

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Q: Differentiate the function. 1,2 g(x) = 6. 6x + 15 | g'(x) = %3D

A: topic - derivative of a function

Q: What is the equation of the tangent line to the function y=x²-1 at a point (2,3)?

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Q: 18) 4y"+4y'+17y=0

A: Given: 4y''+4y'+17y=0 So, we can also write as; 4D2+4D+17y=0 The auxiliary equation is: 4m2+4m+17=0

Q: Find the value of k that will make the function f(x) continuous. -x2+8, if x+ 3 f (x) =, k, if x=3

A: topic - limits and continuity

Q: Let C be the graph of the equation In(3y – 2e") = sinh (ma) - tan(y- 1). dy (a) Find da (b) Find an ...

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Q: 5. For this problem, you have to read and study the textbook pages 762- 763 about The Limit 00 8. Co...

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Q: Consider the funetion 1) Find the domain of glx) 2) Find lim g(x) and limg(x). 3) Find oblique asymp...

A: Solution: Given data ,  g(x)= 2√(x2+3x)

Q: I. Find y', y" and y"" of the following functions. a. y = 2x-x'+ 5 b. y = (r²+2) x-1 II. Use the cha...

A: I. (a).y=2x4-x3+5diff w.r.t xdydx=2(4x3)-3x2+0y'=8x3-3x2diff w.r.t x againy"=8(3x2)-3(2x)y"=24x2-6xd...

Q: 0.3t ug -) of a drug t hours after being injected is given by C(t) : ml The concentration (in Find t...

A: The concentration of drug,Ct=0.3 tt2+38

Q: – 4x + 30 The partial fraction decomposition of can be written in the form of 8x2 + 34x + 21 f(x) g(...

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Q: 10. Vx – 1dx 15 32 32 b. 15 a. 32 d. none of the choices C.- 15

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Q: x+3,if x2

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