Exercise 1: Directions: Evaluate the following integrals. Show your complete solutions. Identify the u and the du of the given. Provide also the formula needed. 1. S 5e* dx

Q: Solve for x. = x + x² + x' + ., ]x| < 1 ... 11 + 11x (Use symbolic notation and fractions where need...

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Q: Using integration by parts and taking a > 0, the integral x In(ax)dx is equal to: In a 2 In(2a) - 3 ...

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Q: -0o (x2 + 1 Evaluate the integral if it converges. Enter the exact answer, or enter na if it diverge...

A: The given integral,      ∫-∞+∞xx2+12dx

Q: -x³ +10x² – 5x+15 -dx x²(x² +5) | 4. Partial Fractions dx 5. Half-Angle Substitution | 3+5cosx

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Q: Let y(t) represent your bank account balance, in dollars, after t years. Suppose you start with $800...

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

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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: Write the general antiderivative. (Use C for the constant of integration.) x2+1 dx 5x Need Help? Rea...

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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: Determine whether the given series is convergent or divergent. +oo 5n + sin? Σ - | sin n| а. 3" n=1 ...

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Q: owner of a ranch has 1900 yards of fencing material with which to enclose a rectangular piece of gra...

A: Given query is to find the dimensions for maximum area.

Q: (D² – 1) y = e-2* sin (e-*)

A: I am attaching image so that you understand each and every step.

Q: Find the Taylor polynomial of degree 3, centered at a 2 for the function f(x) = VI + 5.

A: We will find the Taylor polynomial. 

Q: Using Integral or comparison test, determine if the series is converging or diverging. +00 nyn n² + ...

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Q: Q– Fin the surface area of the portion of the paraboloid z= 6-2x - y that is above the x-y plane (z-...

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Q: Evaluate the integrals of the functions graphed by using the formulas for areas of triangles and cir...

A: Given query is to find the value of the integral.

Q: Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the so...

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Q: Solve the following linear differential equation

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Q: lim ("V52"-1 52n-1

A: F

Q: Verify that the series n4 + 1 n=1 satisfies the conditions of the Integral Test, then use the Integr...

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Q: Consider the function whose graph is shown below. Determine if the function is continuous at the fun...

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Q: For what numbers​ x, −2π≤x≤2π​, does secx=​1? For what numbers x does secx=−​1?

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Q: Determine the following information regarding the function + 2(x - 4)- A. f (x) f "(x) Intervals of ...

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

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Q: Use Cramer's rule to solve the system of equations. If D = 0, use another method to determine the so...

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Q: 7. Let C be the curve y = 3x for 0 <x S 1. 0.5 Find the surface area of revolution of C about the x-...

A: Given: y=3x3 for 0≤x≤1

Q: A new cell phone is introduced into the market. It is predicted that sales will grow logistically. T...

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Q: For the demand function x=D(p)=/100-2p : (a) The elasticity is E(p)= (b) When p=25 , the elasticity ...

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Q: Find the points of Intersection of the graphs of the equations. x+y%= 15 -3x +y%3D 11 (x, y) = (smal...

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Q: 5. Evaluate the folloming integral over the region R 2des places. Gitosetrsine)r dride పా

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Q: A polynomialƒ (x) and one or more of its zeros are given. f(x)=4x - 51x +184x-111 6+i is a zero Part...

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Q: 10x + 1800 The average cost for a company to produce x units of a product is given by the function A...

A: Given: Average cost for a company to produce x units of a product is given by a function A(x) =( 10x...

Q: Write out first five terms of the sequences, determine whether, the sequence converges, and if so, f...

A: We have to find the limit of the sequence and find first five terms

Q: True or False: To evaluate the integral dr, 9. we use substitution withz= 3 sec 0, where Select one:...

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Q: Anote card company has found that the marginal cost per card of producing x note cards is given by t...

A: Given query is to find the cost of prducing x cards.

Q: Determine whether the series converges, and if so, find its sum. E-1(-1)k-1 6k-1

A: topic -  series convergence and divergence 

Q: about lim f(x, y)? (x,y)-(0.0) Using the two-path test, lim (xy)-(0,0) f(x, y) = 1. lim f(x, y) exis...

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Q: he demand, D, for a new rollerball pen is given by D = 0.006p° - 0.4p + 180p, wherep is the price in...

A: Since you have asked multiple question, we will solve the first 3 part of the question for you as pe...

Q: 6. A vertical tank shaped like a truncated square pyramid is filled with water. Find the work requir...

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Q: y=5Xy-2x

A: NOTE: Refresh your page if you can't see any equations. .

Q: Write a Riemann sum corresponding to the following definite integral. p6 sinx 1+ x5

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Q: dy If y = (t² + 7t + 5) (2t² + 6), find dt

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Q: (3tanx-2cosy)sec²xdx

A: We will solve the differential equation. 

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

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Q: Solve the given third-order differential equation by variation of parameters. y'' + y' = cot(x) y(x)

A: First we write complementary solution then find particular solutions then find general solution. 

Q: +00 S" x?dx

A: To write that the given integral is improper or not.

Q: Sketch the level curve of the function y? f(z, y) = %3D 9. 16 for c = 1.

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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: A sample of radioactive material starts with 0 grams . After 3 half -lives have passed , how much ra...

A: Let's find. 

Q: 3. Find the arc length of y = 3x3/2 on the interval 1<x< 3 %3D

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