If g (x) =3x²– 4x+5 ; G(x)=x³ – 2x²+ 5x , then G is the anitiderivative of f . A True False Question 2 x)dx + True False

Q: Evaluate the definite integral 10 (100 – 2²)dx 10

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Q: Express the following limit as a definite integral. n 1 lim Σ -Axg where P is a partition of [2,3] 1...

A: From the definition of the definite integral of f from a to b , we have               ∫ab f(x) dx =l...

Q: VE-Vyt1 Let f : ACR² →→ R be given by f(x, y) I-y-1 Write, if any, the limit below to 4 decimal plac...

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Q: 24 - dx /3- 4x (х + 1) 3.

A: Given that:                        

Q: II. Find the limits of the ff by applying the techniques of evaluating limit theorems. x2 + 4x + 3 1...

A: We can solve the questions to find the limit as below.

Q: 2 50 = 50t Rint 204 Rint %3D

A: Solving the problem by finding the Rint.

Q: f (x).8 (x) ]dx= 8 (x)dx f (x)dx + (A) True B) False

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Q: Question 1 Let f (x) = x³ + 2x³ + 7x + 1 Find (f -1)' (a) for a = 1 . O (f -1)' (1) = 4 O (f -1)' (1...

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Q: The exam has 14 questions, and the total number of marks for the exam is 100. In how many ways can t...

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Q: 4. A student borrowed money from a friend at 5% simple interest to help pay for college tuition. At ...

A: Given, Final amount = $1365 Interest rate = 5% = 0.05

Q: 13) In Problems 13 through 20 given f(x) and g(x) are Continuous and Differentiable EVERYWHERE with ...

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Q: B. Find the slope of the curve at the given point. 1.) y = x? – 5 at (1, -4) 2.) y = 3x? – 4 at (0, ...

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Q: + - 5*) dx 5*+! .In5 +C 5 л+1 A True Ealse

A: Given: - The statement is, ∫(e4-5π)dx=e55-5π+1.ln(5)π+1+C To choose: - The given statement is true o...

Q: 19 Let r be the region in the xy-plane bounded by the curves y=VX and y=X^. Set up, but do not evalu...

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Q: Karen decided to put her money into two investments. She deposited an amount in an investment paying...

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Q: 192 Chapter 3 Differentiatio 27. Sports A baseball diamond has the shape of a square with sides 90 f...

A: Given query is to find the rate of change of distance.

Q: Determine the infinite limit. x2 + 6x lim x-3 x2 – 6x + 9 8

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Q: Evaluate the definite integral: 28z* dz

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Q: Given the function f (x) = tan(3x) with the domain -5,5, choose the correct responses to complete th...

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Q: A roller coaster is being designed that starts at (0, 21) and ends at (24, 1). Along the ride there ...

A: Given query is to find the correct option for the graph.

Q: Solve the inequality and write the solution in interval notation when possible. Express numbers as i...

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Q: 1. lim 3" 2. lim 5* 2 3. lim log r

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...

Q: Use any method to determine if the series converges or diverges. Give reasons for your answer. 00 15...

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Q: 13)Evaluate 13 Evaluate the integral s 5x--Xt27 dx x (x²+G) -1 3 tan 3+C b)(-ト2フx)、1mlxCx?ss)1c Sx3 ...

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Q: II. Evaluate the limits. tan 0 2. lim 0 -0 sin 20 (y-#)* 2. 4. lim t 1-sin y y - 2 2.

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Q: A patrol car is parked 35 feet from a long warehouse (see figure). The revolving light on top of the...

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Q: Find the derivative of the function using the definition of derivative. 1 f(x) = x2 - 16 f'(x) = Sta...

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Q: For a function f integrable on [a,b], its average value on [a,b], also called its mean, is given by ...

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Q: an open box is to be constructed from a poece of cardboard 10 cm by 20 com by cutting squares of sid...

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Q: Find the value of the constant k that makes the function continuous. 2x-2x-12 if x#3 g(x) = x- 3 kx ...

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Q: Find the equation of the line tangent to y = xln (x) at the point (e, e). Write the equation in slop...

A: Given that the function y=xlnx  To find : equation of tangent at point e,eSolution:y=xlnxslope =m=dy...

Q: Section 4-7 : Triple Integrals in Spherical Coordinates 7. Evaluate the following integral by first ...

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Q: Find the present value of $3000 payable at the end of 4 years, if money may be invested at 8% with i...

A: Future value = $3000  Time period= 4years  Interest = 8%  r= 0.08    

Q: a The integral that represents the length of the curve 7 (t) = <2/t,cos (2t3/2), sin (2t3/2)) where ...

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Q: If 2 ak = 4 and E bk = 42, find the following values. k= 1 k= 1 n b Σ 38 Σ Σ E (ak + bx). E (ak - bk...

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Q: Questions: (2 points) Find the tangent plane to the surface of x? + 2² = y? + 9 at (1, – 1,3). 3

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Q: dx the integrand is In x2 (A) True B) False

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Q: f'(x) = Compare the graphs of f and f' and use them to explain why your answer is reasonable. f'(x) ...

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Q: Use the basic properties of the integral to calculate (u² + 6u) du. Si(u² + 6u) du =

A: ∫03 u2+6udu

Q: Given the function f(x) = –3x – 3, express the value of +n-12) in simplest -f(x) form.

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Q: a The integral that represents the length of the curve 7(t) = (2/t, cos (2t3/2), sin (2t3/2)), where...

A: length of curve

Q: Find lim Sin 3x (1- Cosx) メーや。 メ*s X Sinzx cosx

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Q: 1. lim f(x) = -1 and f(1)DNE 2. lim f(x) = 1 and f(0) = -3 lim f(x) = -2, X → 2- lim f(x) = 2 and f(...

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Q: EXERCISES- Section 3.1 1-6 I For each of the following functions and inter- val, find the average of...

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Q: Use any method to determine if the series converges or diverges. Give reasons for your answ (-4)" n°...

A: We have to check Series convergence. 

Q: The length of a rectangular poster is 1 ft more than the width, and a diagonal of the poster is t. F...

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Q: (a) Find the value of k. Is the population increasing or 32. Population The populations P (in thousa...

A: We will find as shown below

Q: The radius r of a circle is increasing at a rate of 7 centimeters per minute. Find the rate of chang...

A: Given query is to find the rate of change of area of a circle whose radius is increasing with rate o...

Q: Which of the following ordered pairs satisfy the inequality 3x+2y= а. (0,0) .Ь. (5,1) с. (0,2.5) • d...

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Q: Implicit Differentiation To find y' given f(x,y) = 0: 1. Differentiate both sides of the equation f(...

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