dx The integral can be rewritten as - X (a) lim (-2 + 2V1-s) (b) lim (-1+ 2v1 -s) S-00 00--S (c) lim (-2+ V1 - s) (d) lim (2 – 2/1 -s) S--00 S--00

Q: 10. Using back calculation, find out what the function f(x) should be so that the second derivative ...

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Q: 25. f(x) = 1 – V

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one. ...

Q: sec (In x) + sec2(In x) tan(In x) 2х Given: dx Find: du tan(in x) 2х sec³(In x) + sec²(In x) sec(in ...

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Q: Evaluate the integral SV5+12x² – 4xª xdx 1 -(5+ 12x² – 4xª) ² +C 24 (2x2 – 3)/5+ 12x? – 4xª + 14Arcs...

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Q: Write an equation for a rational function with the given characteristics. 4, x-intercepts at (-4,0) ...

A: Explained below 

Q: SV + 2) /2 – 3y dy -

A: The detailed solution is given below Thank you 

Q: dx 2V x3 - 3x x

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Q: 3. A single-input, single-output system has the state variable representation *= Ax + Bu y = Cx 1 wh...

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Q: 2x2 + 3r +2 2 +2

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Q: Use the shell method to set up a definite integral (set up only, do not evaluate the integral) for t...

A: (b) the line y = -3 Draw a line segment across the region parallel to the axis of revolution (the li...

Q: 00 k k 2. Σ (- 1)- k+1 k=0

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Q: ку — 1 x²y 1 dx dy = 0 ху?

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Q: What is the resulting integrable form of evx+I x+1

A: We have to find value of given Integral.

Q: Evaluate the following. Use the graph of f(x) to evaluate the following expressions. (4, 5) (1,5), (...

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Q: 11-14 Verify that the function satisfies the hypotheses of the Mean Value Theorem on the given inter...

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Q: Find the Taylor polynomial of degree 3, centered at a 3 for the function f(x) I+ 4.

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Q: f = f (x, y) = u? + 3v, y = uv

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Q: Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 4x2...

A: We will use the fact that  The Mean Value Theorem states that if a function f is continuous on the c...

Q: Find the derivative of the function f(x)=2x−73x−2 at x=2

A: topic - derivative of a function

Q: Scos(cos2x) sin2x dx Given: Find: du О 2cos2x dx -2sin2x dx -2cos2x dx 2sin2x dx

A: The solution is given in the next step.

Q: -5 dx Evaluate 2х — 10 (а) — оо (c) 1/2 (d) 0 00

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Q: e) Explain how one can use differentiation to analytically determine the slope of a curve

A: If cost revenue given , we differentiate it so we give marginal revenue. 

Q: 3 sin? 4t + 8 cos² t

A: Solution: L{3sin24t + 8cos2t} Use the following identity : sin2x=12-cos(2x)12 =L{312-cos(2·4t)12+8co...

Q: Find dydx for y=ln2x3−x2

A: This question is based on derivative.

Q: Let F(z) = | sin(5t) dt. Find the MacLaurin polynomial of degree 7 for F(z). 0.69 | sin(5z*) dz. Use...

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Q: Given: 5e-x-6e-3x Find: u 5e-x - 6e-3x O 5e2x – 6 5e¬x-6e-3x O 5- 6e-2x

A: topic - indefinite integral

Q: Given: J5x2 cos(3x³) dx. If U=3x°, then the resulting integral is Jf(u) du. Find 4

A: I=∫ 5x2 cos(3x3) dxu=3x3du = 9 x2 dxx2 dx =du9which gives;I =∫ 5 cos(u) du9I =∫ 59cos(u)  du .....(1...

Q: Identify all three (distinct) solutions to the equation z3 = 27i. Write your answer in x + iy form.

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Q: 45-56 Find the absolute maximum and absolute minimum values of f on the given interval. 45. f(x) = 1...

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Q: Enter the value of L- 1.27].

A: Floor value of x  is given as the greatest integer that is less than or equal to x

Q: Evaluate x2 + y? – z dS where S is the part of the cone z? = x2 + y² that lies between the planes z ...

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Q: y 4 3 2 -3 -2 -1 2 3 4 5

A: Using simpson rule with n=4 .   

Q: y y = 2 2 1 y = 1 → X п/2

A: The given question has been solved in detail. 

Q: 15-28 Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and m...

A: Maximum and minimum

Q: The area of a circular sunspot is growing at a rate of 500 km/sec. (a) How fast is the radius growin...

A: Note that, the area of a circular sunspot is A=πr2 So,  dAdt=π2rdrdt⇒dAdt=2πrdrdt...(1) Now, given t...

Q: 29-42 Find the critical numbers of the function. 29. f(x) = 4 + x - 30. f(x) = x' + 6x - 15x 31. f(x...

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Q: Consider the improper integral I = dz. 4x +1 (a) Find the value of the constant C for which the inte...

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Q: Find the rate of change of the volume of a cube with respect to the length of its side s when s =3 ...

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Q: 5. Find the limits: a) limg→0 4 – Vx + 16 Vz – 3 b) limz→9 z - 9 t +2 c) lim→-2 |t+2|

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Q: 4x 1.2) lim X4 yx-2

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Q: 5+ 12x2 - 4x xdx a (2x? -3)/5+12x² – 4xª + 14in/2x² - 3+/5+12x? – 4x*|} b H2x2-3)/5+12x² – 4x + 14Ar...

A: To evaluate the given integral.∫5+12x2-4x4 x dx  

Q: 14. Find dr/de: r= 0 sin 0 + cos 0 а. cos @ b. 0 cos 0 0 sin 0 C. O a O b

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Q: 7. Using integration by parts evaluate the integral /(z- 2x)e-3 dz

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Q: The graph of an everywhere differentiable function is shown below. Use it to select the correct ineq...

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Q: Which of the following graphs show a jump discontinuity? (Select all that apply)

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Q: ind the values of c that make f continuous everywhere: { Sa² – c² if x 3

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Q: 19-22 Use a triple integral to find the volume of the given solid 22. The solid enclosed by the cyli...

A: Given cylinder is x2+z2=4 and the plane is y=-1 and y+z=4 So,  y→-1 to 4-z z→-4-x2 to 4-x2 And x→-2 ...

Q: dx Given: Vx sin/x Find: Formula o Sesc u du O2 fcsc u CSC du O 2 sin u du Ssin u du

A: Explained below 

Q: complementry function for this DE  12.7y" + 68.58y' + 153y = 0.289(y+1)

A:

Q: sec3(In x) + sec²(In x) tan(In x) dx Given: 2x Find: du V sec (In x) + sec²(In x) dx tan(ın x) dx ta...

A: On solving this we will get