Find the curvature of the space curve. r(t) = - 3i + (3+2t)j + (t +8)k %3D

Q: The general solution of the fourth-order differential equation y() + y" + y" =0 is: %3D y=c_1 +c_2…

A: The general solution of the fourth-order differential equation.

Q: A. Evaluate the following integrals. 1. fxdx

A: Topic = Integration As per guidelines , At a time only one question can be answered out of different…

Q: In how many ways can Joe, Mary, Steve, Tina and Brenda be seated around a round table? 24 12 20

A: We have to tell number of ways can Joe, Mary, Steve, Tina and Brenda be seated around a round table…

Q: 5. Prove lim,40 V2r +I= 1.

A: Given :limx→02x+1=1

Q: Nathan invested $2,870 for 219 days at a simple interest rate of 2.75% p.a. How much more or less…

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Q: Using decomposition into partial fractions, 4x2 + 2 -dx x(x² + 2) is equal to In|x (x² + 2)| + C…

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Q: y = x' cosx

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Q: The maximum value of x +y subject to the constraint x² + y² = 1 is Write in decimal form (two…

A: We have to find the maximum value of given function.

Q: A) lim x→3−    f(x)= B) lim  x→3+    f(x)= C) f(3)= D) Determine whether the function f is…

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Q: Find the curve length of the function 1 1. f(x) = ;x² 0 < x < 3

A: We can find the curve length as below.

Q: 2 is rational ご -2 x is irpational odd ? even (メ)

A: Given the function,     fx=2,x is rational-2,x is irrational

Q: ropriate substitution, n³ (4x)cos*(4x)dx is equal to

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Q: The length of a rectangle is increasing at a rate of 9 cm/s and its width is increasing at a rate of…

A: Explained below

Q: Find the absolute maximum and absolute minimum for the given function on the ir f(x) = x3 + 3x² – 9x…

A: Topic:- application of derivatives

Q: PRACTICE ANOTHER fence parallel to one of the sides of the rectangle. Let y represent the length (in…

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Q: Evaluate 3x- 2y ds where C is the line segment from (3,6)to(1,-1)ts -58.240 58.240 O -57.991 O Non…

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Q: . The population of a town reaches 113000. 7 years ago the population was 82000. Assuming that the…

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Q: Using decomposition into partial fractions, 4x2 + 2 dx x(x2 + 2) is equal to In/x (x² + 2)| + C…

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Q: Use the Integral Test to determine whether the series is convergent or divergent. -2n ne =1 Evaluate…

A: From integral test of a series we get,   If a function f(x) is continuous , positive and decreasing…

Q: 1 What is the instantaneous rate of change of Y= at x = 2? - o-1 4 O none of these -1 -1

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Q: If In a + In(x- 5) = In(2x), then x = Show your work on paper. Use the space below to upload a…

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Q: (1) (2) (4) B" A" A" B" 90 B'

A: We will find the type of pairs of lines.

Q: 3x2 – 2x – 8 - Let f(x) 3x2 – 11x + 6 - This function has: 1) A y-intercept at the point 2)…

A: Simplify the function using definition of asymptote.

Q: Find the area between the curves f(x) and g(x) 2. f(x) = 3x, g(x) = x² – 3x + 8

A: We will find the area between the two curves.

Q: Using the method of undetermined coefficients, a particular solution of the differential equation…

A: Given differential equation is y''-16y=2e4x. The characteristic equation is m2-16=0⇒m=±4. So, by the…

Q: Find the slope of the function f (x) = x 3 + 3x 2 + 3x + 1 at x = 0 1 0 3

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Q: 1+x dx V1-x

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Q: 8- Consider u=x², v=1/u+1 and w=vv find dv/dx

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Q: Find an equation for the function f that has the given derivative and whose graph passes through the…

A: Given query is to find the the function.

Q: Using Sandwich Theorem, the sequence 1 cos? n + 1 an = 4 - n converges to 4 converges to 2 diverges…

A: Given

Q: If log, (5x + 6) = 5, then x = You may enter the exact value or round to 4 decimal places. > Next…

A: We will solve for x.

Q: \n + 2, The following telescoping series ΣΗ 1 sin sin-1 n + 1 n + 2, n=1 TT converges to converges…

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Q: A particle is moving with acceleration a(t) = 36t + 2. its position at time t = 0 is s(0) = 2 and…

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Q: The following series 3 2n- 4n+1 3n n=1

A: Series

Q: Given the following differential equation (E): y" + 2y' + 5y = 0. The solution of (E) is: O None of…

A: We have to find solution of given differential equation.

Q: sin(x) 1- sin? (x) 3. Evaluate the integral O 2ln|1 - sin2(x)| + C O -csc(x) + C sec(x) + C O None…

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Q: A test has multiple choice questions with 3 choices for each answer; only one answer is correct for…

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Q: dx Vx+2

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Q: can you say about the series a, in each of the following cases? |an+1 lim n- c0 (a) an absolutely…

A: We have to find the convergent test

Q: 6 What is the recursive formula for the sequence 3, -12, 48, -192, 768,...? a 1 = 3, a n = (a n -…

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Q: Without evaluating the constants, the partial fraction decomposition for 5x2 – 3 - f(x) : %3D (x³ –…

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Q: From Rogawski ET 2e section 10.7, exercise 58. Find the first four non-zero terms of the Maclaurin…

A: Given problem:-

Q: Find the angle in radians for the given right triangle. Round answers to the nearest hundredth. 10 7

A: Given angle to find is θThe side opposite to θ is called the Opp side and the side that is longest…

Q: Match equation question type with a graph I- A V%3D (2 - B) (z - A) (z- A) (z - B) %3D

A: Graph: 1: a figure (such as a sequence of one or more points, lines, line segments, curves, or…

Q: Using the Nth term test for divergence, 00 n 5n-2 n2 n=1 diverges since lim V5n-2 n² is equal to O 5…

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Q: (b) Find the values of a andb so that the function f(x) = x2 + ax +b has a local maximum at the…

A: We have to find the value of a and b

Q: cos(xy) + secy = 5

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Q: b) sec(arcsin x2+4, 以a sin g 孙 OPP Los : als hyp a-t6-cと とい ))Not how sec = x-Vxty %3D exponent…

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Q: x-3 Analyze the following limits and find the vertical asymptotes of f(x) = x -9 a. lim f(x) b. lim…

A: The given function,   f(x)=x-3x2-9

Q: x3 + x2 – 5x + 15 dx 5. (x2 + 5)(x² + 2x + 3)

A: Partial fraction: A complicated rational statement is decomposed into two or simpler fractions using…