EVALUATE EACH OF THE FOLLOWING INDEFINITE INTEGRALS. Write the correct u and du. 3edx -16 2.10-3rdr 3. In (cost)

Q: (1+cot 0) de J sin e 4 -cot* 0 5.

A: Given problem:-

Q: Problem 3.1 Prove that if x is a positive real number, then LV[]] = [V]

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Q: -3xdx 8.

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Q: (-1)"+1

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Q: 5. r(t) = (t°/3) i + (12/2) j, t>0 %3D 6. r(t) = (cos³ t) i + (sin³t) j, 0<t< a/2 %3D

A: This question is about finding vectors   k, b &amp; t   

Q: An instructor gives the same y vs. x data as given below to four students and asks them to regress t...

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Q: Evaluate the following integrals: dx 1. Vzax-x2

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: Factor the difference an+1 – an to show that the given sequence {an} is strictly increasing or stric...

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Q: Зх-1 dx; J x²+10x+28 Зх— 1 Sa :dx (x + 5)² + 25' Зх — 1 -dx Ja+ 1)² + 1 Option 3 Option 1 Зх - 1 dx ...

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Q: Find the derivative of the function. y = xe-x8 %3D y' = %3D

A: Given: y=xe-x8

Q: 6.Use a Taylor polynomial of order 2 to approximate the result of the following integral: 2 |(e2x-1 ...

A: We have to approximate given Integral.

Q: The below curve is rotated about the y-axis. Find the area of the resulting surface. x7 y = 1s* 10, ...

A: I am going to solve the given problem by using some simple calculus to get the required result of th...

Q: 31-32 Find an equation of the tangent line to the given curve at the specified point. the x² – 1 iqn...

A: Given y=x2-1x2+x+1 To find equation of tangent line at point (1, 0):

Q: For the function f(x,y,z) = In (6x + 7y + 4z), find fx, fy, and f,.

A: Given: f(x,y,z)=ln(6x+7y+4z)To find the fx, fy, and fzddx (ln x)=1x  

Q: Find the Maclaurin polynomials of orders n = 0,1,2,3, and 4, and then find the nth Maclaurin polynom...

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Q: If f(x) = 2x¬1, then f'(x) is equal to a. x2 b. 1 2x C. 4 x3 d. 4 x3

A: Given :   Discontinuity And f(x)=2x-1

Q: The slope of the tangent line to the differentiable function f at the point (2, f(2)) is [(2+Ax)-f(2...

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Q: On what domain is the function f(x) = 5+ V2x + 6 continuous? %3D

A: Let's find. 

Q: (nx)dy/dx+2y=xy^(n+1) where n is constant, solve using linear equation diff eq

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Q: 1. Given the graph find y (a) f(-4) 6. (b) f(0) 4 (c) lim_f(x) X-4 (d) lim f(x) x→-4+ T ||► x 24 6 (...

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Q: y. -4

A: topic - indefinite integral

Q: Find the critical points for the function f(x, y) = 5æ² – 10zy + 6y? – 6y and classify each as a loc...

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Q: ∫sin8 (3?) cos5 (3?)??

A: Find the what later to come on the symbols

Q: Let h(x) = f (X)g(x). If f (x) = In(3x² - - 4) and g(x) = 3x – 1, what is h' (x)? Select the correct...

A: Here, the given function is: h(x)=f(x)g(x)

Q: Use sigma notation to write the Taylor series about x = xo for the function. 10 In x; xo = 1 %3| Σ -...

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Q: A spherical balloon is inflating with helium at a rate of 128x ft / min. How fast is the balloon's r...

A: We have to find radius is increasing at a rate of and surface area is increase at arate 

Q: Find a parametric equation for the line that is perpendicular to the graph of the equation 2x + y +4...

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Q: 7 Let f(x) = 7 The slope of the tangent line to the graph of f(x) at the point - 3, is The equation ...

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Q: Rank the magnitudes of the directional derivatives in the directions of vectors a, b, c and d at poi...

A: We need to find order of vectors.

Q: 8. Sketch the graph of a sinusoldal functions with the following characteristice • Domain: • Range: ...

A: from the given data we can conclude that sinusoidal function f(x) have peak to peak value =4time per...

Q: Find the derivative of the function. Q(x) = V e8x + x %3D Q'(x) = %3D

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Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: minimize z=4x+6y subject to: 3 0 y > 0

A: We are going to solve the give. Problem by graphical method.  In the shaded region, the linear funct...

Q: To evaluate the / sin-(x) + sin(x) cos2(x) -dx using basic formula of integration (without using sub...

A: We need to find values of f(x).

Q: dy 2.

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Q: At 3:15 pm, a metal ball has a temperature 80°F is taken outside where the air temperature is 20°F. ...

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Q: Sa-1) CX-2xtら)

A: To find the solution of the integration.

Q: For f(x)= 4x and g(x) =x+5, find the following functions. a. (fo g)(x); b. (g o f)(x); c. (fo g)(3);...

A: Given:  fx=4x  gx=x+5 a) f∘gx   we know that      f∘gx=fgx                     =4gx                 ...

Q: cof dv 3. cot ( +9) 1-cos let u= du=

A: Given problem:-

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

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Q: of of and ду For the function f(x,y) = In (7x + 9y), find

A: The given function,     f(x,y)=ln7x+9y

Q: Ssin (x) + sin(x) cos²(x) To evaluate the dx using basic formula of integration (without using subst...

A: This question is based on indefinite integral.

Q: 4. p² –1) cos[cosh (In r)]dr let u= du=

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Q: 33-34 For what values of x does the graph of f have a horizontal tangent? Hercnt 33. f(x) = x + 2 si...

A: we have f(x) = x+2sin x

Q: Find (f o g)(x) and (g o f)(x). f(x) = 4x² – 1; g(x) == (fo g)(x) =| %3D (Simplify your answer. Do n...

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Q: +o0 S 13 In n n=1 Determine whether the sequence converges, and if so find its limit. If the sequenc...

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Q: I+6 et f(z) = if I = 7 22 if z> 7 ompute the quantities below. Write "DNE" if the limit does not exi...

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Q: (c) Find the area of the region common to the interiors of the cardioids T = 1+'cos 0 and r = 1- cos...

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Q: Find an equation of the tangent line to the parabola y=x2+x such that it passes through the point (2...

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Q: x³ – - 3x 2x² 5. lim X--5 x² - x

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