Explain why Rolle's Theorem does not apply to the function even though there exist a and b such that f(a) = f(b). (Select all that apply.) f(x)= cot x/2, [pi,7pi]

Q: Sv 8x – 16 dx=2 x- 2dx A True B False

A: Show that,∫8x-163dx=2∫x-23dxAnswer:-4LHS=∫8x-163dxLet 8x-16=udifferentiate8dx=duTherefore LHS=∫u38du...

Q: 2 x+1 -dx . Evaluate:

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Q: In order to evaluate the integral expression / In( sin(x) ) dv using simple substitution, dv=f(x)dx_...

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Q: where: y = child's dose c = age of child in years a = adult dose Computation of the derivative of y ...

A: here,  y=acc+12dydc=-ac2+11ac-12a(c+12)2  

Q: 3. 2yy' = x² +1 4. (x2 – 1)y³dx + x²dy = 0

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Q: If u <0, then -in (-u) +C u (A) True B False

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Q: Ni dr A +1 B 2 C) D E) None

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Q: Question 16 Evaluate: SVX+ sin/x dx. A) None of the given choices 2x+ cos/x + C B 2 x+2cosx +C Ox-2c...

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Q: tan( tan3x)dx Evaluate: cos²3x A 3 -In sec(tan3x)| + C B -n|cos( tan3x)| + C In|cos (tan3x)| +C (D D...

A: the given integral,      ∫tan(tan 3x)dxcos23x

Q: x--x+1 Evaluate: dx A 2,½_2,½-22+c 3 B 2 2 2

A: We have to find out the solutions

Q: Find the exact value of the expression. cot

A: Cot(x)= Cos(x)/Sin(x)

Q: Given cost and price​ (demand) functions C(q)=110q+40,400 and p(q)=−1.8q+890​, what profit can the c...

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Q: Question 19 Evaluate: / (secx - tanx)-dx A none of the given choic B 2secx - 2tanx -x+C © 2secx - 2t...

A: Given: ∫secx-tanx2dx  

Q: 2x²+ 2x+1 x+1 Evaluate: e dx. 1 + C X +1 A) x² + x +1 x+1 n|x+ 1| + C B - + In|x+ 1| + C D x2 + In|x...

A: The given integral is; eln[(2x^2+2x+1)/(x+1)].

Q: Question 11 dx 4+e (A) 4+e* (B) e ot D 4e*+1 E) None

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Q: If sin(t) = and t is in quadrant II, find cos(t), sec(t), csc(t), tan(t), cot(t). cos(t) %3D csc(t) ...

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Q: 3. A piece of wire 36 in. is cut into two parts, one of which is bent into the shape of an equilater...

A: It is given that, the length of the wire = 36 in. It is cut into two pieces. Let the length of the o...

Q: cos0 + tan@ ) đo | (secô + tandsec²0)d0 cos²0 со A) True B False

A: On solving this integration we will get

Q: Find the correct u and du then find the equivalent.

A: All option given is in terms of x only but i correct for variable u and t. 

Q: In(/5+ x?) +c Match the integral expression on the left with its appropriate value. Prompts Submitte...

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Q: Match the integral expression on the left with appropriate dV so that the antiderivative will exist....

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Q: If f and g are the functions whose graphs are shown, let u(x) = f(x)g(x) and v(x) = f(x)/g(x). %3D r...

A: here f(1)=2,g(1)=1,f(5)=3,g(5)=2 Lets find f'(1),g'(1),f'(5),g'(5): for 0≤x≤2 f'(x)=∆f∆x=4-02-0=42=2...

Q: To evaluate the integral expression / sin -1(Vx ) dv, using simple substitution dv =f (x)dx_ Determi...

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Q: tan –15t sech Evaluate: 1+2512

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Q: 2w²+9w+ 1 dw is the same as w +4 A dw w +4 2w +1+ 3 dw w +4 B 2w – 1 - 3 dw w+4 2w +1- 67 dw w +4 2w...

A: Given that           ∫{(2w2+9w+1)/(w+4)}dw

Q: 3 sin 2 tsin2tdt (A sint 3 B sin 2t c) cost (D) sin2t E None

A: Indefinite Integral: 

Q: 1. A closed box, with a rectangular base, whose length is twice its width, is to have a surface of 1...

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Q: dx V2x+1 A 2/2x+1 +C B ® V2r+1+C (2+1) 24 C D

A:

Q: Se 2x2+ 2х +1 dx. х+1 Evaluate:

A: We will solve the integration. 

Q: - (sin(Inx?))² Which of the following is equivalent to the integrand of | dx? A None of the given ch...

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Q: dx 5+ x2

A:

Q: 4 x2 + 4

A: We have to find out the antiderivative

Q: -dx (use 2 decimal places, no space) 5+x Let x = 3.63, and y = 4.58. Determine the value of C when y...

A: we have given∫xx+5dx and also given x=3.63 at y =4.58

Q: find u and du. show

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Q: Suppose that the cost (in dollars) for a company to produce x pairs of a new line of jeans is C(x) =...

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Q: `In²(Ine*) dx (A) Inx B In'x Inx2 D Ine" None

A: integration

Q: dx In then the integrand is the same as 4e +1 4+e A) True B) False

A:

Q: Evaluate: tan(4x +3)dx A 4 A -In |cos (4x + 3)|+c B -In |sin(4x + 3)|+C 1 (c) -In |csc (4x+3)|+C D -...

A: integration

Q: xdx 5+ x 2 X

A: Here,             We have given an indefinite integral                now we have to solve this and ...

Q: 2x2+ 2x+1) In Evaluate: e x+1 dx. 1 + C X+1 (A) X+ (в x2 + In|x + 1| + C None of the given choices ²...

A:

Q: Match the function on the left to its appropriate antiderivative on the right. Prompts Submitted Ans...

A: 1) I=∫14-x2dx Let, u=x2, Then, x=2u  and   dx=2du now, the intergal becomes: I=∫14-(2u)22du I=2∫14-4...

Q: 4. у %3D х6 - Зх4 + 5x2 7 2 4 6 8 5. у %3D (x + 10) (2х - 5) 6. у %3D (x3 + 1) (3x2 - 1) 7. у %3D 5x...

A: We have to find the derivative of the following function

Q: Suppose that f(4) = 4, g(4) = 3, f'(4) = -2, and g'(4) = 5. Find h'(4). (a) h(x) = 5(x) + 3g(x) h'(4...

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Q: / (cos0 + tan@ ) dô | (seco + tandsec20) do cos20 A True B) False

A: Left Hand Side    =∫cosθ+tanθcos2θ dθ                   = ∫cosθcos2θ+tanθcos2θ dθ             =∫1cos...

Q: A graphing calculator is recommended. x² - 1 Let f(x) = x2 + 1 (a) Find f'(x) and f"(x). f'(x) = f"(...

A: Here, the given function is: f(x)=x2-1x2+1

Q: What is the relative minimum value of the the function f(x, y) = e+v ? Note: If the answer is a nega...

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Q: - ydx + (x++ xy )dy = 0

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Q: Evaluate: [Vx+ sin/X d. A 2x+ cos/x + C 2 (B) x- 2cos/x + C 2х- cos/x + C 2 D x+2cos/x+C E None of t...

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Q: Assume that all variables are implicit functions of time t. Find the indicated rate. dx dy x+4y +4y ...

A: The given function,x2+4y2+4y=49; dxdt=2 when x=7 and y=-1

Q: 12. A company produces a special new type of TV. The company has fixed costs of ​$470,000​, and it c...

A: