2x ind the derivative of: 2e cos(8x). [Hint: use product rule and chain rule!] se e^x for e*. ow, find the equation of the tangent line to the curve at x = 0. Write your answer in mx + b format. =

Q: 3. (D2 + 2D + 1)y = 0; when x = 0, y = 1, Dy = - 1.

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Q: Given A (В B [²₁f(x) dx = 0 and 11 6 11 5 55 6 √ √ ² f(x) dx = 11 6 0 evaluate 0 [²3f(x) dx - ₁2f(x)…

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Q: CALCULUS 2 1200-1330 TTh CALCULUS 2-FINAL TERM Exam 90 minutes remaining Oi Test Content Question 1…

A: Solve it

Q: Evaluating √9-x² dx using trigonometric substitution will lead to: -3 A 355/20 cos²0de 0 **/2 B Ⓒ 18…

A: Evaluate using trigonometric substitution ∫-339-x2dx=?

Q: Solve the integral: A 5n/1+x²|+C 5 (B) 6in 5+x' 6In|5+ +C 음 m/1+x²|+c C ³√|+C 1+x √√√√x+x² dx D

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Q: Evaluate the improper integral (A) diverges (в B (C) ml+ 2 3 √√2²233/3dx 4

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Q: dx Transforming - using miscellaneous substitution will yield to secx + 1 A -dz 1+z² B 1² 2-2z² 1+z²…

A: Given problem:-

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Q: Question 1 Solve the integral: Seln(2x²+3x-4)³ (4x+3)dx A eln(2x²+3x-4) (4x+3) 3(2x²+3x-4)…

A: To evaluate the given indefinite integral.

Q: dx Evaluate: (x+1) log(x+1) (A) -In[log(x+1)]+C In 10 B In 10 In[log(x+1)] + C © In 10 log2 (x+1) +…

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Q: Determine the area bounded by f(x)=x²-x and x-axis. 2 A unitz Ⓡunit² unit2 1 D 4 -unit²

A: We will integrate the f(x) between limits 0 to 1.

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: Given that g be a differentiable function and the range of g be an interval I.  f is a function…

Q: To evaluate the integral sin ³0cos 0d0 by trigonometric transformation, we use the identity; A…

A: ∫sin3θcos6θ dθ

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x) =…

A:

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A: If fx and gx are integrable on the closed interval a, b, and k is a constant, then to determine wich…

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Q: Determine the integral: x²cosxdx A x²sinx + 2xcosx-2sinx + C B x²sinx + 2xcosx + 2sinx + C…

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Q: Evaluate the integral: Se³+ cosh2x33+ cosh2xsinh2x dx 3+ (3e)3 + cosh2x A + C 2+2ln3 (3e)3 + sinh2x…

A:

Q: Evaluate the double integral: 2 √² √ (3x² +9y²) dxdy A 40 B 30 C 60 D 80

A: Double Integration by iteration:

Q: Find the volume of solid generated by revolving the region bounded by f(x) = x² + 1and g(x)=x²+2x+…

A: Let's find volume of solid.

Q: integral sin ³0cos Odt sin20 2 sin²0 = 1 - cos²0 1+ cos20 cos²0= 2 1- cos20 (D) sin²0= 2 To evaluate…

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Q: Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u 9…

A:

Q: Question 23 en [ "_f(x)dx=0 and ["f(x)dx = 1, evaluate Given A 0 B (u) D 11 76 55 =¹3f(x) dx -…

A: We have to find out the integral

Q: Evaluating √√9-x² dx using trigonometric substitution will (A) 18 18 [*/2 cos²0d0 0 **/2 B 0 Cab…

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Q: Solve the integral: 1 √√√√√x+x dx

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Q: Determine the area bounded by the functions f(x) = (x + 1)³ and g(x)=x+1. A unit² B D H|m -unit² 3 q…

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Q: dx (x+1) log(x+ ) In[log(x+1)] + og² (x+1) + C

A: We have to choose the correct option from the given options

Q: COS (+3 O cos x Ocos 2x O sin a Ocos z +x) + cos (-) is equivalent to:

A:

Q: (x2y3 - 1+) dx + x3y2dy = 0 1+9x2

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

Q: Determine the area bounded by f(x)=x²-x and x-axis. A unit² ® unit² Ⓒunit² 1 D unit²

A: topic - area bounded by curves

Q: (x+1) dx (x+2)(x-1)² = √ [+²2 S₁ B + - - 1 + x-1 (x-1)2 ]dx. the values of A & C respectively are:

A:

Q: Stretching spring: Eighteen pounds of force is required to stretch a spring 3 ft. from its natural…

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Q: sinh x + ex cosh x + ex In the indefinite Integral in(cosh x + ex)- dx, what is the integrand?

A: Intergrand

Q: If f(x) and g(x) are integrable on the closed interval [a, b], and k is a constant, which of the…

A:

Q: Question 3 In the indefinite Integral in(cosh. x +ex). sinh x +e* (A cosh x + ex sinh x + ex In(cosh…

A: The integration are

Q: √²² (3x² +9y²) dxdy Evaluate the double integral: (A) 40 (B) 80 Ⓒ30 (D) 60

A:

Q: Let g be a differentiable function, and let the range of g be an interval I. Suppose that f is a…

A: Given that g(x) is a differentiable function and range of g(x) is interval I. f(x) is a function…

Q: (в B f(x)g(x) dx = [ f(x) dx g(x) dx]

A:

Q: Find the area bounded by : f(x)=e*, g(x) = e¯* and x=3. A (e²-1)² e² sq. units B (e³-1)² e3 sq.…

A: The region bounded by the curves f(x)=ex, g(x)=e-x and x=3

Q: S Let the integral be 'solvable' using trigonometric substitution. What is the correct choice of u…

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Q: If 8(x) = [e²-m (21+ - dx S[e²-In (21+1) ]dt, find g(x). -2 A e-In(2x+1) 4 B (2x + 1)² 2 Ⓒ (2x + 1)²…

A:

Q: In S₁² = 10 A (1,00) B (-∞0,00) c) (-∞,1] D {0,1} Given -dx, determine all value/values of P for…

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Q: Question 17 The improper integral A 00 B) e C) 0 (D) 1 if the 0 edx is

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Q: Given f(x)dx =0 and f²f(x)dx = 끝. 11 A 6 55 B 6 11 C 5 D evaluate S" 3f(x)dx - [2f(x)dx.

A: Here, given that: ∫-11f(x) dx=0, ∫01f(x) dx=116

Q: If $S₁ A B (x+1) dx (x+2)(x−1)² 9 3 D -la 1 9 I -ja 2 3 2 93 12 93 ==√ [= ²4/2+1 B x-1 C (x-1)² ]dx…

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Q: B C) + et. + 4 (2x + 1)² 4 (2x + 1)²

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Q: To evaluate the integral sin³0cos0de by trigonometric transformation, we use the identity; A sin²0=…

A:

Q: Which of these expressions represents the area bounded by y = 1/2 x^2 and y = 3x? * 6x + x²dx 6x…

A: To solve the following problem

Q: Using disk method, find the volume of the solid generated by revolving the R bounded by y = 3(2 − x)…

A:

Q: U 4. Let f(x, y) = ey, where x = uv, y = a) Use chain rule to compute and af af Əv ди b) Express…

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