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Q: The derivative of the function y = e* In(cos x) is: y' = e*(In(cos x) – tan x) y' = e*(In(sec x) + t...

A: To find the derivative of the following function.y=ex lncos x

Q: 20 -1 3. sin

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Q: The graph shown below is fx) = -(x - 1)2 + 5. What is the integral function g(x) that defines the ar...

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Q: Find the volume of the solid obtained by rotating the region bounded by y = x , y = 0, a about the y...

A: Given query is to find the volume finthe solid generated.

Q: i. Comment whether the sequence is Converges or diverges. ii. Obtain the first five terms of that se...

A: We know sequence is convergent when limit of sequence is finite

Q: Using an appropriate substitution, cos x-sin x the integral dx equals: 2 cos x+sin x -1 none of them

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Q: 3. For every 100 ticket buyers at a concert, the band expects to sell 27 T-shirts. a. If they have s...

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Q: g3 (*° – 2x² + 1)dx 9. Evaluate the definite integrals (give exact answers): •3 a) | (2x+3)(x – 5)dx...

A: Given that, There are two integral given, a). ∫23(2x+3)(x-5)dx b). ∫121x3(x3-2x2+1)dx We have to fin...

Q: Using an appropriate substitution, e*sec²(e*) the integral S dx equals: e-tan(eX) - In|e – tan(e*)|I...

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Q: Find the acceleration of the potato at 0.5 s ft/s?

A: s(t)=-81t2+225t+3acceleration a(t)=s''(t)consider s(t)=-81t2+225t+3Differentiate with respect to ts'...

Q: Evaluate: / cot-12 e Sa dß. ß cot-12B – In|1+482| + C A B cot-128+ -In| 1+482| + C 8 ß cot-12B+ In|1...

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Q: find the afproyimate Value of: (3.01)*+(5-98)²+(2.03)?

A: solution

Q: y = ecos²(x) is: eCos? %3D y' = - sin(2x)ecos²(x) y' = sin(2x)ecos²(x) the above the above y' = -2 s...

A: Here we will find the derivative of the given function,

Q: Evaluate: S,(3y6 + 8y* – 9y?)dy 2

A: ∫-223y6+8y4-9y2dy

Q: Find F' (÷) if F(x) = 2 cos-1 Vx. %3D

A: We will find the value of F'12 where Fx=2 cos-1x in the following step.

Q: Exercises: Find the general solution of the following differential equations 4) y"+2y'+y=3e*

A: Given

Q: alculate the curvature of the vector function when t=0.1: 7(t) = (e", V2t, et)

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Q: Let lim an = a and lim bn = b. Therefore n-00 n-00 ii) lim anbn = ab, n-00

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Q: 14 If f(x) = /* t² dt then f'(x) =

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Q: 2x + 4, a<4 om the following results, determine whether the function f(a) = { 8, a = 4 -x + 16 a 4 i...

A: Given query is to find function is continuous or not at x = 4.

Q: Using an appropriate substitution, cos x-sin x the integral Jo cosx+sin x dx equals: 0 cosx+sinx 1 -...

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Q: Evaluate the integral. (Use C for the constant of integration.) | 2 csc*(x) cot (x) dx

A: We will use simple Integration formulae to solve this Integral.

Q: Consider the following function RX) - 9x - 7 Determine whether the function is even, odd, or neither...

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Q: You deposit $2000 in an account earning 5% interest compounded continuously. How much will you have ...

A: topic - exponential function

Q: Use integration by parts to evaluate the integral: for 9t sin(t)dt

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Q: Find || (x, y) dA where f(x,y)=y and Ris the region bounded by y = x² and y = x. (A) (c) (B) 12 15 r...

A: Given: I=∫∫Rfx,ydA ; fx,y=y And y=x2 &amp; y=x   As we know that; The Power rule: ∫xndx=xn+1n+1+C ; ...

Q: A pharmaceutical company is testing a new drug. After a person takes Ao mg of the drug, the amount o...

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Q: 4. 2(x + 4) = - 4 5. -3( x + 4) = 15 6. 4(2х + 3) + х%3D69 7. 2x + 3x + 6 = 31

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Q: 23. y + ху %3 ху , У0) %3D 3

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Q: Which of the following best describes the function below? S(x)={3r if.rs2 |x³ if 2<x f(x) =: A. Cont...

A: To check continuity we find left hand limit and Right hand limit. If they are equal then function is...

Q: A potato is launched vertically upward with an initial velocity of 139 ft/s from a potato gun at the...

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Q: Check if the field is conservative, if so, calculate by the Fundamental Theorem of Calculus for Line...

A:   F =2xy i +(x2+2yz) j + y2 kcurl F=ijkddxddyddz2xy(x2+2yz)y2      =(2y-2y)i-(0-0)j+(2x-2x)kcurl F =...

Q: Find the global minimum of the function f (x) 1 + x² on the interval (0, co0)

A: Given that f(x)= 1+x2.  And we find global minima on the interval (0, infinity).     Here i attached...

Q: DO NOT include spaces in between characters. * Given F(x)= f(x)g(x) and f(2) = -3, f'(2) = 4, g(2) =...

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Q: The graph shown below is Ax) = 2 cos x. If g(x) = Sðf(t)dt , find g '( ). %3D %3D 4 3 54 32 -14 1 23...

A: The function is given by fx = 2cosx The graph of the function is  To evaluate: The value of g'π if ...

Q: For the demand function q= D(p)= 346-p, find the following. a) The elasticity b) The elasticity at p...

A: Given q=346-p

Q: Using an appropriate substitution, 8tan-1x the integral J dx equals: 1+x2

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Q: Remember: 1- Distribute 2- Combine like terms 3- Cancel with addition or subtraction 4- Cancel with ...

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Q: 1. Complete the following tables of values to investigate lim(x? - 2x + 4). S(x) f(x) 0.5 1.6 0.7 1....

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Q: Which of the following functions form a particular solution of the differential equation y"+y = sinx...

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Q: az az Find and e = 5x 2² + sin(r + 2) – y?.

A: Find the partial derivative of z with respect to x and with respect to y respectively

Q: Evaluate the integral, if it exists: lim sinx dx r→+z -r

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Q: Evaluate the integral. 16 In(y) dy Vy

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Q: The derivative of the function y = sin-1(ex – In x), where Je* – In x| < 1, is:

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Q: DO NOT include spaces in between characters. Type your answers in the following order and format: a=...

A: Given query is to find the value of a and b.

Q: DO NOT include spaces in between 10 characters. * Evaluate f'(-2) if ƒ(x) = x* – 5 + x-2 + 4x-4. %3D

A: Solve the function

Q: Which integral would represent the area shown below? The function is f(x) = 2x + 2. 8 6 4- 2- 0.5 1 ...

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Q: Find the global maximum of the function f (x) 2x³ + 3x? – 12x + 4 - on the interval [-4,2].

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Q: Consider the parallelepiped with adjacent edges u = 7i + 3j + k v = i+j+ 7k w = i+ 5j + 7k Find the ...

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Q: Find the global minimum of the function f (x) = 2x’ + 3x² – 12x + 4 on the interval [-4,2].

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