For x1/2 dx and using the substitution = x 1/2, the resulting integral takes the form: 4u -du -du -du A / ® / VI B © / S D 4u 4-(2²) 2 -du

Q: Estimate the slope of the tangent line to the curve at the given point (-3.5,1.250) on the graph to…

A: In this question, we want to find the slope of the tangent line of the curve at point (-3.5, 1.250).

Q: Find the area bounded by the trigonometric curves O2.828 square units 1.414 square units 3.667…

A: topic - area bounded by curves

Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? 1/2 3/8 1/4…

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Q: Evaluate sin sin (Inx) dx. Integration by parts will be used repeatedly. What is the expression…

A: Integrating By Parts : ∫u.v dx =u∫v dx -∫dudx∫v dxdx

Q: Evaluate only four integrals of the following integrals: 1/4 1 dx (i) dx (ii) J √1-9x² sin (3x) 0…

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A: The problem is to find volume of solid generated by curves revolving about a line using disk method.…

Q: 5л Find the area bounded by the trigonometric curves y=sinx and y=cosx from x= to 3.459 square units…

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Q: Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after the…

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Q: 2. Find the interval [a, b] for which the value of the integral (2 + x − x²) dx is a maximum.

A: ∫ab(2 + x -x2 )dx here for get maximum value we have to differentiate the function  so here first…

Q: Evaluate sin (1 sin (Inx) dx Integration by parts will be used repeatedly. What is the expression…

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Q: For the following exercises, find aj dt and direct substitution. 225. f(x, y) = ln(x + y), x=e¹, y =…

A: Given;  f(x,y)=ln(x+y), x=et, y=et.

Q: Consider the function f(x) = x² - 9x + 20 x - 3 a. Find the first derivative. f'(x) = b. List any…

A: We have to find the derivative and monotone intervals.   According to our guidelines we can solve…

Q: ·S- x² + sece tane de sece - 1 e integral sec²0 de 1+tan cose de 1-sin sine de S x dx can be…

A: We have to find the integral

Q: Evaluate Stan" (x) see³x dx

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Q: a) A vector equation of a line that goes through the points P(1, -3, 2) and Q(9, 2, 0)

A: topic- equation of line

Q: 2x+1 (b) g(x) = f(x)

A: We want to find the differential of g(x)

Q: Evaluate S tan" (x) sec¹x dx. I A tan (+1)(x)tan (-1)(x) + C m+l - 1 I B tan (+3)(x) +tan (+1)(x) +…

A: Let's evaluate given integral.

Q: Newton's Law of Cooling a) A cup of coffee has temperature 95° C and takes 30 minutes to cool to 61°…

A: SOLUTION-

Q: The volume of the solid generated by revolving the region bounded by x2=4y and y²=4x about y=4 is to…

A: Here, the region is bounded by the curves x2=4y⇒x=4y & y2=4x which is rotated around y=4 axis…

Q: T/6 3 coss 3x dx

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Q: To evaluate x²cosx dx' use integration by parts. What is the expression after the second integration…

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Q: dx The integral can be transformed to which of the following when trigonometric substitution is…

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Q: Consider ·S= x-m+- Sx 3x5 -dx. Using the method of partial fractions, the given integral can be…

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A: We have to find the inner radius

Q: 18

A: We will solve the problem

Q: S ' | Sc Sex²0 The integral dx (x²+4)² see c³0 de s²0 de csc ³0 de sin ²0 de can be transformed to…

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Q: Consider x sinx cosx dx = f(x) sin2x - g(x) cos2x + C. What is the value of f(1) + g(1)? (A) 3/8 B)…

A: We have to find out value

Q: Question 2. Find the limit, if it exists, or show that the limit does not exist. (a) 4xy (2,3)—(0,0)…

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Q: 16. Evaluate the integral or show that it is divergent dx x+1 1 (a) √ (3x+1)³², I (3+1), (b) /…

A: We need to find out here  integrals.

Q: Evaluate sin (Inx) dx Integration by parts will be used repeatedly. What is the expression after the…

A: We have to find ∫sinln(x) dxWe will apply formula for integration by parts.We know, ∫uv dx…

Q: In this problem, you are asked to carefully read Example 6.4.2 of APEX Calculus. 1 The given…

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Q: If f(x) = 10, find f'(-1).

A: Given f(x)=10,  to find f'(-1) Formula used Differentiation of a constant value is zero d (constant)…

Q: The volume of the solid generated by revolving the region bounded by x2= 4y and y2=4x about y=4 is…

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Q: Use linear approximation to estimate the amount of paint in cubic centimeters needed to apply a coat…

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Q: Find an equation of the line tangent to the graph of f(x) = (4x-7)(x+4) at (2,6). The equation of…

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Q: The volume of the solid generated by revolving the region bounded by x2=4y and y2=4x about y=4 is to…

A: Solution is here

Q: x1/2 S dx and using the substitution = x 1/2, the resulting integral takes the form: x-x³ U A / du U…

A:

Q: Find an equation of the tangent line to the given curve at the specified point. = (1, e) X y =

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Q: Use polar coordinates to find an iterated integral for finding the volume of the solid enclosed by…

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Q: QUESTION 14 To evaluate use integration by parts. What is the expression after the second…

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Q: Use the method of elimination to evaluate the determinants

A: Question number 16 has been solved as per the request of the student.     This question can be…

Q: Let f(x)=2-3√. Then the expression can be written in the form where A, B, and C are constants.…

A: Solved below.

Q: What is the value of f(1) - 16B in [x³ Inx dx = f(x) ((1/4) Inx-B) + C?

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Q: N|- x² Given: quadric surface S with equation (y - 3)2 - 2 (a) Determine and identify the traces of…

A: Quadratic surface S with equation y-32-x22-z22=1

Q: The volume of the solid generated by revolving the region bounded by x²=4y and y2=4x about y=4 is to…

A: Given:  Region x2=4y             y=x24               y2=4x                y=4x                 y=2x…

Q: dx ·S can be transformed to which of the following when trigonometric substitution is used? (x²+4)²…

A: Solution is here

Q: Solve the system of differential equations. 80 X' x 5 x₁ (0) 9, ₂(0) = 7 x₁ (t) = rolt)

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Q: What is the value of f(1) - 168 in x3 Inx dx = f(x) ((1/4) Inx - B) + C? 02 8 8 0 3 1

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Q: Use the limit definition of the derivative to find the instantaneous rate of change o ƒ(x) = 5x² +…

A: We have to find rate of change

Q: The polynomial function f is defined by f(x) = −2x² + 3x³ + 5x²-x-5. Use the ALEKS graphing…

A: We need to find local maximum.