π/4 x³ dx (x²+4)5/2 (Use trigonometric substitution)

Q: I. Evaluate the following limits. Using L'Hôpital's Rule is not allowed. 2. lim (√²-x-√√x² + x)

A: The given limit,     limx→-∞x2-x-x2+x

Q: Find polar equation for the Cartesian equation 13y = 8x. a. theta = 1.02 c. theta = 0.55 d. r = 0.55…

A: Substitute x=rcosθ and y=rsinθ in 13y=8x. 13rsinθ=8rcosθ  13sinθ  =  8cosθ

Q: 7(e)₁² X y= » - [1-171² 2 sec- y = (tan 17 1² ² X y = [cscx]arcsin (cos.x)

A:

Q: -2√4x²+k

A:

Q: List the absolute maximum and absolute minimum of f(x) = x³ 12x on the interval -3, 1]. Give the…

A:

Q: Water is dripping into a hemispherical bowl with a radius of 8 cm at a rate of 1 cubic cm per…

A: Volume is evaluated.

Q: Find T(t) and N(t) at the given point. x = T(0) N(0) = = = e cost, yet sint, z = e; t = 0

A:

Q: [sin³() cos(4) dx (A B C) D 32 32 3/² cos (4) + 3 cos (4) + C 5 32 3 cos (4)[-5cos² (4)+7] 35 32 35…

A:

Q: Describe the graph of the equation. r = 7 cos ti - 9 sin t j + k major axis of length 7 parallel to…

A: We need to describe graph of given function.

Q: List intervals on which the following function is INCREASING. Use INF for infinity, use no spaces,…

A: The given function,    fx=3x2-1

Q: 4. Determine the limits: a) b) 4x²-8xy lim (x,y)-(2,1) (x²-xy-2y², lim (x,y) → (0,0)…

A:

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: Given the function f(n) = 3n¹ +33n³ +90n²: its f-intercept is its n-intercepts are

A: We can find the intercepts as below in the following steps.

Q: The radius of a circle increases at a rate of 2 m/s. Find the rate at which the area of the circle…

A:

Q: Given: (1+2x) ex dx. Using integration by parts and letting u = -1-2x, dv = f(x)dx, then the value…

A:

Q: S Find sec42x -dx tanº2x cot²2x-cot82t+C 12 16 1 1 1 1 12 tan 62x 16 tan 82x --(cot$2x) (² 1+3csc²2x…

A:

Q: Given: (1+2x) e-x dx. Using integration by parts and letting u = -1- 2x, dv = f(x)dx, then the value…

A: Let's find.

Q: 4x /² sin () cos (+) sin (²) dx (Consider initially the first 2 terms) 3

A:

Q: 7. f(x) = 3√x; [1,4] 8. f(x) = x-2/3; [1,27]

A: We can solve this as follows:

Q: 1. f/² sin (1) cos (4) Sir sin (²) dx (Consider initially the first 2 terms)

A:

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

A:

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: Consider using the method of partial fractions to solve x²+x+1 rb Sa 2x²+2+x²+x - dx = [Af(x) – B…

A:

Q: Logarithm function Copy the table onto your paper, and fill in the x-values for y = log, x. x y -1 0…

A:

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

A:

Q: Summary of Derivatives of Transcen Let u be a differentiable function of z du (a)(e) =eu dr (b)(b) =…

A: To express the derivative of transcendental functions.

Q: √√√x²-9 Consider x³ what is the integral form in terms of? 1 A Scos²e de B Scos²e de Ⓒ-S sin²e de C)…

A:

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: . The voltage,V, in a circuit is slowly dropping at a rate of -0.01 volt/sec as the battery wears…

A: I have appended the formula used in the solution part.

Q: x³+x A. -1 dx = f(+ g(x)) dx, then A+ B. -1 + In(5/2) C. 1 dx, then A + f²g(x) dx is equal to D. -1…

A:

Q: Sketch a graph of f(x)=(x-2)² +4 6.

A:

Q: - In(x - 2) + 3, X

A: answer is in next step

Q: Find f'(1) given that f(x) ax+b cx+d' where a, b, c, d are constant.

A: we have to find derivative.

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

A:

Q: Consider the function f(x) = x² x7 +4 Use the Intermediate Value Theorem, if applicable, to…

A: Using the intermediate value theorem.

Q: dx 5. Evaluate the following tanº(x) cos4(x) tan'(x) [7tan²(x) +9] + C 36 tan(x) + =tan(x) + C…

A:

Q: 1. A. B. C. D. dx If f is solved by trigonometric substitution, the resulting x²-2x-4 integrand is?…

A:

Q: y=x√1 + x²

A:

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)…

A:

Q: 14. Evaluate the following √x-²sec (+)tan ³ ( =) « dx 2tan (²) [7tan² ( ² ) +11] +C 77 2tan…

A: To evaluate: I=∫x-2sec41xtan521xdx Substitute 1x=t⇒-1x2dx=dt⇒x-2=-dt So, I=∫sec4t  tan52t…

Q: A B C The IBP formula fudv=uv-fvdu can also be written as f udv + ſ vdu : = UV Which of the…

A:

Q: Find an equation of the surface of revolution by revolving the plane curve 3y = √(9- [(x-1)] ^2)…

A:

Q: Explain why you think the sequence converges to a finite number or (n+1)! diverges. If the sequence…

A:

Q: S 1 xvx²-2x dx = √x²-2x X +C

A: To prove that ∫1xx2-2xdx=x2-2xx+C

Q: π/4 ²dx (x²+4)5/2 (Use trigonometric substitution)

A:

Q: b) Determine whether the series n=1 find its sum. Show All Your Work! n-1 (-3)* 4" is convergent or…

A: We need to determine convergence.

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

A:

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

A: A detailed solution is given below

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

A:

Q: (A) = and B D = . Find the vector projection of A onto 2A - BO O O O none of the above

A: