Find all the roots of the following function f(x) = (x2 + 5)(2x4 -10x2 + 8)

Q: Consider the curve C parametrized by x = t and y = (36 - t2)1/2 for -6 ≤ t ≤ 6 Write an equation…

A:

Q: Let f(x) = -0.72-6.16 if -0.51z -3.53 if -3

A:

Q: Find y' 2x-3 y= 3x + 1 y"=0

A:

Q: Consider the following. sin³(y) cos (y) dy ---Select--- This is an integral of the form sin(y)…

A:

Q: 35. y = w² sin w+ 2w cos w 2 sin w 36. y = -x³ cos x + 3x² sin x + 6x cos x − 6 sin x 37. y = 38. y…

A:

Q: T 5. lim ex x →0

A:

Q: 11. lim (In (3x+1)-In (2x² +1)) X-∞

A: To evaluate the following limit without using derivatives or L’Hospital rule.

Q: Find all values of c such that f is continuous on (-∞, ∞). 7-x², f(x) = { }, C = C = x ≤ c x>c…

A: Here  function is given. Now we need to find all the values of .Now we will use the definition of…

Q: 2b) f(x) = 2x²-1 4 2c) h(x) = (2x − 1)4(4x − 3)³ 2d) h(x) = (x²+1)² (2x²-3)²

A: Differentiate the function

Q: (5) Alex plots the price per share of a stock that he owns as a function of time and finds that it…

A: S(t)= t(20-3t)+30We have to find average price of the stock over first five years

Q: (4) Find the average value of each function on the given interval. (a) f(x) = x(x²+1)7, [0, 1] (b)…

A:

Q: Evaluate each of the following indefinite integrals. Use capital letter C as the constant of…

A:

Q: A 500 gallon tank initially contains 200 gallons of water in which 100 pounds of salt have been…

A: We have to find the amount of salt in the tank at the moment when the tank overflows.

Q: (a) Find the inverse function of f. f-1(x) = (b) Graph fand f-1 on the same set of coordinate axes.…

A:

Q: If lim f(x) = 5, must f be defined at x = 1? If it is, must f(1) = 5? Can anything be concluded…

A: Given the limit expression at x tends to 1.

Q: Find an equation of the tangent plane to the surface at the given point f(x,y)=x²-2xy+y², (4,9,25)

A: The equation of the surface isThe point isTo determine: The equation of the tangent plane.

Q: Let j(x) = x 1 3 x Determine the values of x for which j has a vertical asymptote. If multiple such…

A: Consider the function

Q: Answer the following problems show your complete solutions 4√2-3 lim 2-9/16 162-9

A:

Q: (2) Use integration by parts to evaluate the following definite integrals. (a) [² (1-x²) e³² dr (b)…

A:

Q: 4. Find the solution of the system whose augmented matrix is 1 1 202 3 4 2 1 102 2

A:

Q: The altitude of a right triangle is 10 cm. Let h be the length of the hypotenuse and let p be the…

A:

Q: Evaluate the integral. I'w ² w² In(w) dw

A:

Q: 1 lim x+22x - 3 = 1 lim √√x²-3 = 1 x→2

A:

Q: Solve differential equation: xy’’=y’

A: Given:   xy'' = y'

Q: 3. Recall that a function of the form f(g(x)) (also written (fog)(x)) is called a composite…

A:

Q: a 1. The matrix J is given by J = C a) Show that J² = d -C -b] 2]. a d where a+d=-1 and ad-bc=1. b)…

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

Q: The number of foreign language teacher jobs in the United States for the 2022-2023 school year can…

A:

Q: f(x) = lim x-0 = Estimate the following by evaluating f at x-values near O. (Round your answer to…

A:

Q: Answer the following problems show your complete solutions. DO NOT USE Hospitals Rule 4√2-3 lim…

A:

Q: Find the Standard form of the equation of the circle with center (-3,3) and the tangent to the line…

A:

Q: Solve the following exponential functions 22x-4=8

A:

Q: 3 -1 5 3 35 m+n -2 where I is a 3x3 identity matrix. Find the values of mand n. 12 2. Given that the…

A:

Q: Sketch the region R whose area is given by the iterated integral. IT. 3- 2- 1- 9 8 7- 6- 5- 4- 3- 2-…

A:

Q: Use an iterated integral to find the area of the region. bb dy dx = 3 2- 1 2 3 X 5 (5,3) 6

A:

Q: (1). Does the following series converge absolutely, converge conditionally or diverge? (a). Σo(7)".…

A: According to our guidelines, we can answer only the first question or first three subparts of a…

Q: Use integration by parts to evaluate the following integrals

A: (d) the given integral Since 5 is constant with respect to x, move 5 out of the…

Q: Part a) Given the graph of f(x) below, evaluate each of the following limits. Ax) lim_ƒ(2) DNE * lim…

A: The existece of limit at

Q: Verify that the Intermediate Value Theorem applies to the indicated interval and find the value of c…

A:

Q: Problem 4: A cylindrical tank contains 500 gallons of water. A plug is pulled from the bottom of the…

A: Using given model, we can solve all the parts.Note : According to our guidelines, we can answer only…

Q: You want to make an open box from a rectangular piece of material, 15 centimeters by 9 centimeters,…

A: DimensionsLength = 15 - 2xWidth = 9 - 2xHeight = x

Q: Determine the intervals on which is continuous. Enter the solution using interval notation. h(z) =…

A:

Q: Consider the following function. f(x) = x = 7 Determine whether f(x) approaches ∞ or -∞ as x…

A: The given function .The aim is to find the limits  and .

Q: Find the derivative of the function using the definition of derivative. f(x) = 3 + 6x - 9x² f'(x) =…

A: The given function is The definition of derivative

Q: lim √x-3 DNE X-3

A:

Q: Solve for inequality and graph 7t-5>5t-4

A: Given inequality 7t-5>5t-4We have to solve it and graph it.

Q: 9. lim ln (1-cos x) x->0

A: To find:-

Q: Find the derivative of the function using the definition of derivative. 1 x² - 25 f'(x) = f(x) =…

A:

Q: (1) tan tan 39

A:

Q: represent the number of bacteria (measured in millions) at time t (measured in hours). This system…

A:

Q: Find the following limit. lim_ f (x) x⇒-4 -10 -5 O ● O 10 5 -5 -10 5 10 A

A: This is question of limit and continuity here limit of function we have to find further calculation…