Question 9 Using trigonometric substitution to solve: cos x dx f 3 (4-sin²x)2

Q: (A) = and (B) = . Find 2A - BO* none of the above

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Q: Find the volume of the solid obtained by rotating about the y-axis the region bounded by y=2x^2-x^3…

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Q: To evaluate S (In x)² -dx, apply integration by parts twice. For the second application of…

A: Follow the procedure given below.

Q: B C 1 x2-9 Consider S +3 - dx. Using trigonometric substitution, what is the integral form in terms…

A: Given: I=∫x2-9x3dx   ...1   As we know that the trigonometric identities; (1). tanθ=sinθcosθ (2).…

Q: Let z+5 f(x) x+7 f¹(-6)= A

A: Topic:- function and it's inverse

Q: Assume f(x) is a differentiable function such taht f(1) = 3, f'(0) = 2, and f'(-2) = 7. Evaluate the…

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Q: 3. Using trigonometric substitution, what is 1 sec-²¹ ( 137 ) + √x²-9 2x² + C A. 1 300² (2) √²-90…

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Q: Evaluate the definite integral. Joe²¹i+ i+e¹j+t kdt kat O © 2²² ² x i 2 © (e²-1) e² O e²-1 2 O e²…

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Q: Given: S√-x² + 4x+5 dx. Using trigonometric substitution, what is the integral form in terms of ? 9…

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Q: tan6(x) cos4(x) sin²(x)sec³(x) [7sin²(x) + 9cos²(x)] + C A 63 tan²(x) [7tan²(x) +9] + C B 36 Ⓒ…

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Q: What is the slope of the tangent line at (0,3) to the function f(x) = -sinx+3

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Q: Question 5 A) O B) 48 32 D) 96 If f cos+2t dt = At - B sin 2t cos 2t + D sin 4t cos 4t + C where A,…

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

Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: 2-1 dy y2-2y-1

A: Explained below

Q: Find the value of the constant C for which the integral 5 1² (√x²³²+ 16- X ³+ 4) ax (v dx converges.…

A: We have to find C .

Q: dx secx+1

A: Given ∫dxsecx+1We do half angle substitution:=∫1tan2(x2)+11-tan2(x2)+1dxSubstitute…

Q: Given the price-supply function p = S(x) = 10(e0.02x - 1), find the average price (in dollars) over…

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Q: 55. f(x) = x² + cos ¹x on [-1, 1]

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Q: 7. Determine all relative extrema or saddle points: f(x, y) = 4x³ + 8xy - 2y²

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Q: rem, if applicable, to determine if f(x) takes the value 0.1 for some x in [0, 1].

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Q: x³ dx Using integration by parts to solve f √4- - 1x², and letting u = - then v = = f(x) is : ...

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Q: Eliminate the parameter and write the resulting rectangular equation whose graph represents the…

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Q: 1 x√x²-2x =dx : √x²-2x x =+c C

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Q: Find the area of region bounded by the graphs of the equations. a. X b. y = x + sin x y + 3 2 1+ -R…

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Q: f(x, y) csc(y) Arcsin (x²) find fx (x, y) and fy (x, y).

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Q: A Ⓒ Using integration by parts to solve f √4x²+k -2√4x²+k -√4x²+k 2√4x²+k x³ dx √4-x² and letting u…

A: Let's find.

Q: In 2 Use the formula t= that gives the time for a population, with a growth rate k, to double, to…

A: We need to find growth rate and time to double the population.

Q: Find E (p) for the price demand equation and interpret the results. x = f(p) = 1200(50p) where p-$28…

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

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Q: Evaluate the definite integral. NOTE: Enter the exact answer. L²||ti ti = + t²i||dt

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Q: Using trigonometric substitution, what is 2 A sec-1 (3) - x²-g 6x² ® 1/1 sec - ¹ (1/3) - B x²-9 2x²…

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Q: Find the area of the region that lies inside the first curve and outside the second curve. r = 6 - 6…

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Q: tan(x) dx cos4(x) tan'(x) A [7tan²(x) +9] + C 36 1 ℗tan'(x) + tan³(x) + C C D sin²(x)sec³(x)…

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Q: What can you say about the series Σan in each of the following cases using the Ratio Test? Answer…

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Q: d. Find an equation of the normal line to the graph of y = √x + 1 at the point (3, 2).

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Q: The demand for a product is given by D(x) = 150e-0.025x, where x is the number of units sold each…

A: Let's find.

Q: 1. Evaluate the following limits. Using L'Hôpital's Rule is not allowed 3. lim (x-3) tan(9-x²)…

A: We will calculate the limits by Limits rule

Q: y=√√√5-√x

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Q: For the function f(x) given below, evaluate lim f(x) and lim f(x). X18 8118 -x³ + x f(x) = √4x6 - 3…

A: We can solve this as follows:

Q: Question 9 y Determine the domain of the function f(y) = (5y-4)²-81 Domain - [yy + } Write your…

A: For domain, we will check for what values function is not defined.

Q: ) Encuentra la inversa de la función f(x) = 4x² – 1 3x² = x < 0.

A: The given function is f(x)=4x2-13x2 We first replace f(x) with y. y=4x2-13x2

Q: dy II. Find Do not simplify your answers. dx ㅠ 1. log;(√2æ² + y) + tan(xª — πª) = sin¯¹(x² − 1) + ½…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Calculate the derivative. f(x) = 6 - 9x¹/3 +9ex (Use symbolic notation and fractions where needed.)

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Q: X A b B a C) C D d is solved by trigonometric substitution, which of the following (b) x = √5 sec8…

A: We can solve as follows

Q: b. The region R enclosed by the curves y = x and y = x² is rotated about the x-axis. Find the volume…

A: Given that region is bounded by the curve y=x and y=x2first find the intersetion point of the curves…

Q: Consider the integral f sin-¹x dx. If we let u = sin ¹x and dv = dx, the integral can be written as…

A: The given integral,  ∫sin-1x dx

Q: Consider using the method of partial fractions to solve x²+x+1 Sa 2x²+2+x²+x A In(x²+1) B x+2 D…

A: This is a problem related to integration of the function using partial fraction decomposition. Based…

Q: 1 xVx+3 xp:

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Q: Find the average value of the function over the given interval and all values of x in the interval…

A: Let's find.

Q: Calculate the derivative. f(x) = (6e* - 7x²) (x³ + 1) (Use symbolic notation and fractions where…

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