Differentiate the function, and find the slope of the tangent line at the given value of the independent variable. 5 f(x) = 4x + = X x = 5 5 The derivative of the function f(x) = 4x + The slope of the tangent line at x = 5 is A is

Q: e the linear inequality. Express the solution using interval notation. 2(8x1) 14x + 10

A: We will find the required.

Q: Find the third derivative of f(x) = = 15x +1.

A: Solve the third derivative of the given function

Q: Suppose that the price p, in dollars, and the number of sales, x, of a certain item are related by…

A:

Q: 59. lim (x - 1)Inx X-1+

A:

Q: Compute the limit In(n²) lim n→ In (2n)

A: Given query is to find the limit.

Q: An automobile tire manufacturer collected the data in the table relating tire pressure x (in pounds…

A: Here is the solution:

Q: Find the Tim X 70 XttanX Sin X limit.

A: We have limx→0x+tanxsinx L'hospital Rule for limx→afxgx=limx→af'xg'x if its 00, ∞∞ etc forms

Q: Suppose f(3) = 4 and f '(3) = 5. Find the indicated values of the derivatives of the following…

A:

Q: 3. Solve for y" for 2x² - y² = 2. 4. Solve for second derivative in the equation tan y = 5x + 3.

A:

Q: Suppose that f(x, y) = x³y². The directional derivative of f(x, y) in the directional (−1, 1) and at…

A: f(x,y)=x3y2point is (2,-2)in the direction of (-1,1)

Q: Find the tangent plane to the equation z = = 4y cos(6x - 5y) at the point (5,6,24)

A:

Q: Model the data using an exponential function f(x) = Abx. x 0 1 2 f(x) 600 1,200 2,400 f(x) =

A:

Q: ntegrate the following function with respect to x using partial fractions: 2x - 3 x2 – 5+6 and hence…

A:

Q: 37. lim x-0+ 39) lim log₂ x log₂ 3x In(x - 2) 2 x→2+ ln(x² - 4)

A:

Q: -0.0136t I A certain radioactive isotope decays according to the formula A = Ape where A₁ is the…

A: A=A0e-0.0136twe know  lnxn=nlnxlne=1

Q: Given h(x) tangent line to h(x) at x = -1? = -2x³ +=; x (A) y - 1= 5(x - 1) (B) y-3-7(x + 1) (C) y -…

A:

Q: Let p=25-√√x and C(x) = 290+4x, where x is the number of garden hoses that can be sold at a price of…

A: (a) Consider the given information. The profit function and the cost function is px=25−x and…

Q: Solve the system of linear equations. -x+4y+z= 9 x - 2y4z = 9 -2x - 3z = 14 O (-1, 3, 4) O (-1, 3,…

A:

Q: 1. (a) (b) (c) Find the general indefinite integral. f(x. (x + tan x) dt 1.9 [(e² +x¹.⁹ + 7x².5) dx…

A: We have to find the indefinite integrals.

Q: wing function, find f'(a). n equation of the line tangent to the graph of f at (a, a=4

A:

Q: Write the composite function in the form f(g(x)). [Identify the inner function u = g(x) and the…

A:

Q: Consider the series S1 = S2 = S3 n = 1 (a) Find the partial sums S₁, S2, S3, and s4. Do you…

A:

Q: Solve for w. Enter your answer as a comma-separated list. 9w³ + 4w² 15W + 1 W = = 0

A: 9w3+4w215w+1=0

Q: Let the region R be the area enclosed by the function f(x) x³, the horizontal line y = -3 and the…

A:

Q: Evaluate the following integral over the Region R. (Answer accurate to 2 decimal places). SS5(x+y)…

A:

Q: Consider the following. x = ln(t), y = 5√t, t≥1 (a) Eliminate the parameter to find a Cartesian…

A: graph

Q: Using the function y=1+2x/x graph the derivative and antiderivative so that the maximum value of the…

A: SOLUTION :-   Given, a function f(x) =(1+2x)x= (1x+2) To find the derivative of given function ,…

Q: fn(z) = ². Determine the pointwise limit lim fn for x > 0 n-x

A:

Q: Find the derivative of the given function. (Remember to simplify the numerator of your answer, but…

A: z(t)=t2+5t+2t+7d dt(tn)=ntn-1d dt(ab)=b×dadt-a×dbdtb2

Q: Find the Fourier series for the following. f(t) = |2t| -π<t<π

A: We need to find the fourier Series of function f(t)= 2t on the interval -π&lt;t&lt;π

Q: d² + a²y = 0 y dt²

A:

Q: An advanced experimental rocket program is terminated after only 7 rockets were produced. The…

A: Here we have to choose the correct option.

Q: Consider the function f(x) = 12x5 + 60x¹ - 100x³ +2. f(x) has inflection points at (reading from…

A: function

Q: R/4 4. ST¹ x sin 2x dx

A: To Find : ∫0π4xsin2x dx

Q: 3) A communication signal is given by the function y = 2sin 3t 405 The task is to: a) Derive and…

A:

Q: Given the graph of f’(x) how to find where f(x) is concave down

A:

Q: Verify the identity sin 2? / (sin 4?) = 1/2 sec 2?

A: We have to verify a set of trigonometric identities.

Q: 8. A fast food restaurant determines that the cost C and revenue R for x hamburgers an be…

A: We need to find out the profit function and also the critical point and maximum or minimum at that…

Q: The total cost function of a company for producing x units of products is given by C(x) = 0.0002 ³…

A:

Q: esc Safari File Edit View History EM Plus Size TikToker ANGRY She's Too Heavy For H... Question 1 >…

A:

Q: Separating the variables in the equation ye ΧΟ A. ydy = xe dx B. ydy = xe da C. None of these. The…

A:

Q: Let f(x) = x² + 3x 2x + 5 Then we have that f'(x) = (2x+5) (A) — (x² + 3x) (B) (C) ² Which…

A:

Q: Let f(x, y) = (x - xy²). In this problem, you will find the absolute maximum and minimum values of…

A: (a) To find critical points, we need to solve for the gradient of f(x, y) and set it equal to zero:…

Q: Consider the function f(x) = 3x³ - 4x on the interval [-3, 3]. Find the average or mean slope of the…

A:

Q: Find the local maximum and minimum values and saddle point(s) of the function. You are encouraged to…

A:

Q: R 4.ry³ dA, where R = {(x,y) € R² | − 1 ≤ x ≤ 1, −2 ≤ y ≤ 2}

A:

Q: Evaluate [²(x² + by the method of integration by parts. (x + 1)e dr

A:

Q: Find the 36th derivative of f (x) = sin2x. Enclose arguments of functions in parentheses. For…

A:

Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

A:

Q: Company produces two products (A and B) that are processed on two assembly lines. Assembly line 1…

A: