lf f(x) = 3x sin x cos x, find f'(x)= To two decimal places, Find f'(2) =

Q: 12) Find the area Under the curve y = e = from X=0 to

A:

Q: . Find a formula for f(x) iff(x) = ln(x - 1). (Hint: x-₁=(x-1)^¹')

A:

Q: Find a formula for the nth term of the sequence. 1, 4, 9, 16, 25,... Determine the sequence's…

A:

Q: The auxiliary equit of the given diff- egnn is m²r² + 6m +8 = 0 2 m²+ ym + 2m +8=0 m (m+4) +2(m+y) =…

A:

Q: dx 1. Find the general solution of + dy y+ xy² + x³ x+x²y+y³ = 0 using DE with IC

A:

Q: Estimate the slope of the tangent line of the function y(t) = √√/4t + 1 at the point t = 3. (Use…

A:

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = √5 -x, 3 ≤ x…

A: We know that surface area obtained by rotating the curve y=f(x) about x axis between x=a & x=b…

Q: f(x, y) = -(x - 7)² In² (y + 4)−(4x + 7y)². a) Find all the first partial derivatives of the…

A:

Q: Find the slope of the tangent line to the graph of f(x) = √√√x-2 at x = 6. Provide your answer…

A:

Q: Find the general solution of the following differential equation. y" + 15y' + 56y = 0 NOTE: Use c₁…

A:

Q: 3. Find the F. T. of the following periodic signal H -2 -1 2

A:

Q: Question vector equation r(t)=. Show that the point Let C be a curve defined by the P(-5, 11, ¹) ies…

A: Solution of given question is written in below steps.

Q: 4. Find the area of the surface formed by revolving the graph of f(x) = x² on the interval [0,…

A:

Q: Evaluate the limit using the Basic Limit Laws and the limits lim, tp/q = cpla and lim,→ck = k. (Use…

A:

Q: Find the determinant of the matrix by reducing A to a triangular matrix. A = -1 2 3 1 1 2 1

A:

Q: Find the minimum distance from the point to the plane x - y + z = 6. (Hint: To simplify the…

A:

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A: Given the functionfx=x2+2xx≤14-x1<x<3x-3x≥3we discuss about the discontinuity of the…

Q: Justin leased equipment worth $70,000 for 5 years. If the lease rate is 5.75% compounded quarterly,…

A: calculation of lease payment are as follows

Q: You plan to save money for a down payment of $38,0 can only afford to save $6,000 at the end of…

A: Topic:- compund interest

Q: Determine whether there is a relative maximum, a relative minimum, a saddle point, or insufficient…

A: Here we have to choose the correct option.

Q: Evaluate f cos*x sin² xdx. 1 16 A B O A 1 -x+ sin 4x 48 1 =x+ 16 1 8 sin 4x 1 64 1 sin³ 2x + C sin³…

A: We need to evaluate integral.

Q: Consider the system of linear differential equations We want to determine the stability of the…

A:

Q: Question 7 of 10 Evaluate lim 2-2 0 x-2 5x-2-√√/2x+4 / Ə

A:

Q: The auxiliary equit of the give is +6m +8 = 0 m ² & 4 mt 3m

A: We are asked to solve the equation

Q: Find y' if y= 6 4 5x

A: I have stated the used formula in the solution

Q: f(x) = 2x + 5

A:

Q: A company manufactures running shoes and basketball shoes. The total revenue (in thousands of…

A:

Q: Identify any extrema of the function by recognizing its given form or its form after completing the…

A:

Q: Assuming that the equations define x and y implicitly as differentiable functions x = f(t), y =…

A: This question is based on differentiation of parametric equation. Slope, m = dy/dx = {dy/dt}/{dx/dt}

Q: For the next three exercises, determine whether the integral converges or diverges. 1+ sin a S 3 71…

A: Let's solve given integral is converges or diverges.

Q: the auxiliary equit of the given diff- eqnn is m² +6m +8 = 0 2 m²^²+4m+ 2m +8 = 0 (m+ y) +² (m+4) =…

A:

Q: 3. Analyze the continuity of this function. If there are discontinuities, state the type. [x² + 2x…

A:

Q: 1. Consider the function f given by f(x)=√ √Int²-1dt 1 Compute the length of the curve y=f(x) from…

A:

Q: Supposed z varies inversely with t and that z= 15 where t =12. What is the value of z when t =3? Z=

A:

Q: To evaluate the integral 3 100 + x² -dx, which of the following substitution shou be used? Select…

A:

Q: Find all relative extrema and saddle points of the function. Use the Second Partials Test where…

A: Let f(x, y)  be a function of two variables. A pair (a, b) is a critical point of 'f' if either…

Q: Determine the domain of the function of two variables f(x,y)=√√y + 3x. The domain is {(x,y). (Type…

A: To determine the domain of the function of two variables fx, y=y+3x.

Q: Find the absolute minimum of the function f(x)= = 02 GW/N 0.3 4 O 1 0-2 01 2 2x x2 +4 on the…

A:

Q: Suppose that a tank with a capacity of 90 gallons initially contains 60 gallons of pure water. A…

A: NOTE: Refresh your page if you can't see any equations. . w=amount of salt(in pounds) at time t…

Q: x= 4+² +7, y=t, t = -1 Write the equation of the tangent line. What is the value of dx² d²y dx² at…

A:

Q: Are the partial derivatives and gradients of a function the same, no matter your starting position?

A: Topic:- application of derivatives

Q: Find the relative maximum and minimum values. f(x,y) = x³ +y³-21xy Select the correct choice below…

A:

Q: For the following left-endpoint Riemann sum, given Ln as indicated, express the limit as n → ∞o as a…

A:

Q: r(t) = (-2 cos (2t), 3 sin (3t), ln (2t)), then the fr(t)dt is equal to 3 -cos (3t), tln (2t) - t) +…

A: Here we find the correct option,

Q: Question show that the limit does not exist. a Find the limit, if it exists, or b) lim (x,y) →(0,0)…

A:

Q: b. On a 6 foot long shelf filled with books, the function B models the distribution of the weight of…

A:

Q: Find the equation of the tangent line to the graph f(x)=x^4 +2x^2 -x at x=1. Write your equation in…

A:

Q: Find c such that f(c) equals the average value of f(x) = 4x + 6 over [-7, -2]. Provide your answer…

A: Given: f(x)=4x+6

Q: Find the indicated value of the function f(x,y,z)=2x-7y + 4z³ -7. f(6, -5,3) f(6, -5,3)=

A:

Q: For the polynomial below, -2 is a zero. f(x)=x² - 4x² - 6x + 12 Express f(x) as a product of linear…

A: