Write an equation for a rational function with: Vertical asymptotes at x = -4 and x = 1 x-intercepts at x = -3 and x = 4 y-intercept at 7

Q: 21n|sinh (1/2 »)|+C

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Q: Let bn and Cn for all n e N such that n > 2. Determine whether the given n = COS = COS n – 1 series ...

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Q: Evaluate the integral .8 xV x+1 dx

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Q: Evaluate the integral. Answer should be expressed as a decimal value (5 decimal places, example 0.01...

A: Put y =5secthetha and solve it. 

Q: 6. Use the Method of Substitution to find the indefinite integrals: et*dt b) /; 9 xp=

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Q: Exercise 7. Let (1 3 0 A = 30 1 0 1 1 1. Find the eigenvalues and associated eigenvectors of A. 2. C...

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Q: +00 Σ 4 Determine if the series converges or diverges. If it converges, find its sum. n² + 4n + 3 n=...

A: ∑n=1∞ 4n2+4n+34 ∑n=1∞ 1n2+4n+3 an =1n2+4n+3Applying series comparison test;1n2+4n+3<1n2checking c...

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A: Given interest is compounded annually, therefore n=1

Q: Using an operator , solve the following differential equations d2y/dx2- 10dy/dx + 25y= 0

A: This question is based on solution of differential equation using D operator.

Q: 1-cos 3t 1. Evaluate lim by constructing table of values. 3t t -1 -0.5 -0.01 -0.001 f(t) 1 0.5 0.01 ...

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Q: Nicholas hopes to earn $600 in interest in 3.3 years time from $24,000 that he has available to inve...

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Q: A particle moves along the x-axis (units in cm). Its initial position at t=0 sec is x(0) = 15. The f...

A: Acceleration

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Q: The range of the function f(x, y) =16-4x² -9y is equal to: [0, 4] [0, 16[ O This option O This optio...

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Q: 7. y= tan e+ e

A: This is a problem of differentiation of the function. By using general formula of the differentiatio...

Q: Consider the function f[x) 3x“ on the interval 7. Find the average or mean slope of the function on ...

A: Given query is to find average rate of change and value of c.

Q: explanations

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Q: True or False: If 3 In|x-3|+B In|x+2|+C (x-3)(x+2) then B = 5 Select one: O True O False

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Q: 3. The diagram shows a cuboid that is formed by bending a long wire of length 336 cm?.

A: Given : h = 4(21-x) x = 12.92 cm  

Q: The integral dz is equal to 2e + C. Select one O True OFalse

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Q: Verify that the series nº + n=1 satisfies the conditions of the Integral Test, then use the Integral...

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Q: Eliminate the parameter: I = sin 3t, y = cos 3t, 0 <t <T/3. = COS

A: x= sin 3t     and y=cos 3t     for    0≤t≤π3 We need to eliminate the parameter i.e. we have to elim...

Q: Write the equation for a sphere centered at the point ( 10, 10, – 8) and has the point (9, 1, 6).

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Q: The population density r miles from the center of a certain city is p(r) = 5e 0.1r people per square...

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Q: To evaluate the integral xp Jx²+5x+6 S we use the partial fraction decomposition of the integrand. S...

A: Find your answer below 

Q: Find the average value of the function f(x) = (1+æ*) over the interval [0, 2]. Select one: O None. O...

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Q: u = 2i + 3j + k v = i+j+ 4k w = i+ 3j + 8k

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Q: Let f(x) = (x - 3)-2. Find all values of c in (1, 4) such that f(4) - f(1) = f'(c)(4 - 1). (Enter yo...

A: topic - mean value theorem

Q: A recipe calls for 3 cups of liquids, which includes ½ cup of lemon juice. What part of the liquid i...

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Q: A) Evaluate the integral Jf(x) dx. B) Find the average value of the function f(x) over the interval ...

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Q: Show that the equation x – 18x + c = 0 has at most one root in the interval [-2, 2].

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Q: I Find the second derivatively") of the following functions and simplity the final results. 1. y=x-x...

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Q: 3. Determine whether each of the following series is convergent or divergent using the appropriate t...

A: a) summation of  n/(n3 + 1). b) summation of (n2 + 1)/(n3 + 1). c) summation of n3 / 5n.    

Q: 1. Find the first derivative the function g(r) = 6x + 54x² + 90x. = (x),6 2. Find the second derivat...

A: Given:- g(x) = 6x3 +54x2 +90x To find:- g'(x)  g''(x)  g''(-1) 

Q: Find the open intervals on which the function f(x) = ax² + bx + c, a ± 0, is increasing and decreasi...

A: Given f(x) = ax^2+bx+c, a is nonzero differentiate withe respect to x df/dx = 2ax+b for increasing d...

Q: -3 dx /2 х-1

A: The given integral,        ∫23dxx-1

Q: To evaluate the integral 4+2a dr, we use Select one: O Substitution with a = 2 sin 0, where Substitu...

A: Given :∫4+x2dx

Q: To evaluate the integral dz, we use Select one: Substitution with z = 2 sin 0, where 2 O Substitutio...

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Q: 9 y= Arctan( 1-2x

A: Use simple differentiation twice to get the answer.

Q: 10) An area is approximated to be 14 in using a left-endpoint rectangle approximation method. A righ...

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Q: 3 sin (x) 4- V1-x2

A: Since you have asked multiple question, we will solve the first question for you. If you want any sp...

Q: Use an appropriate test to determine if the series ) 2n converges or diverges. n+ en

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Q: Suppose f(x) is continuous and increasing on [a, b], and concave up on (a, b). Is T6 (the Trapezoid ...

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Q: Tork Problems [. Evaluate the integral xV x+1 dx

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Q: Use the integral test to determine if the series converges or diverges. Σ 1 5 n=1 (n + 2)7 8.

A: This is a problem of series and sum calculator. By using integral test we will identify the nature o...

Q: 4. Starting from the same point, Royden starts walking eastward at 0.5 m/s while Nilo starts running...

A: Draw a schematic diagram of given question.

Q: diverges, Determine if whether the converges sequence it's limit it Converges state a), 5 (I +

A: 1)an=1+1n9limn→∞1+1n9limn→∞1+1n9limn→∞1+limn→∞1n9(1+0)9 =1limn→∞ {an} exists and is finite.Hence, t...

Q: Use the First Derivative Test to find relative (local) maxi points, if any, of the given functions. ...

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Q: find the moment of inertia with respect to x-axis of the region bounded by y^2=4x and x-1=0

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