2. Find the first derivative of each function: a/y = x³e; b/y = log6 (2x² - 3x + 6); c/ y = e2x cos 5x ; d/ y= (1 - In 6x) ¹⁰.

Q: Question 3 A rectangular box has a perimeter of 50 inches. Find the length and width of the box that…

A: Given :- A rectangular box has a perimeter =50 inches

Q: Given below are descriptions of two lines. Line 1: Goes through (−12, 50) and (−3, 14) Line 2: Goes…

A:

Q: If a company has total costs C(x) = 24,000 + 45x + 0.3x² and total revenues given by R(x) = 425x -…

A: The total cost function is Cx = 24,000+45x+0.3x2 Total revenue function is Rx = 425x-0.7x2 To…

Q: 15. lim x-0 17. lim t->0 19. lim x-0 √1 + 2x 5¹ - 3¹ t et 1 2 x² X X √1 4x

A:

Q: Consider the equation 4x - 9y = 18 A line parallel to the above line would have a slope of A line…

A:

Q: Evaluate the integral. (Use C for the constant of integration.) √ 8 tan³(x) sec(x) dx

A:

Q: Find the area of the unbounded shaded region. 3 (x - 1)³ -∞0 < x < -1

A:

Q: What is the area between the curves y = -²³ and O 10 -24

A:

Q: Find the Taylor series at x = 0 for the function by calculating three derivatives and using the…

A:

Q: Evaluate sin (‡) dxdy- -π/2 cy² 1

A:

Q: Find the 4 th Taylor polynomial of f (2) = Ti ( z ) - N s ( 2 ). If zg= 0 COS N

A: Solving the problem

Q: dt t² - 8t + 20 +2

A:

Q: In Problems 6-10, let R be the region bounded by the semicircle x =√√4-y² and the y-axis. Each…

A:

Q: O Make a graphical tool to approximate the limit of the function. If necessary, round to three…

A: The limit of a function can be found by using the graph or by finding the table of values to the…

Q: Decide whether the integral is improper. [In(x²) dx O proper O improper Explain your reasoning.…

A: The integral is  ∫1∞ ln(x9) dx

Q: 8 3 + 8 2 + 18 3 3 + 8 3 +. ...

A:

Q: . Find the length of the segment indicated. Round to the nearest tenth if necessary. 49 7

A: To determine the value of x

Q: Integrate by partial fractions: x² - 4x + 4 r(r - 1)³ -dx

A:

Q: For the function, evaluate the given expression. y) = \n(x² + y²), find g(0, e) g(x, y) g(0, e): =

A:

Q: For the differential equation: = sin(z)y, what is the slope at (0,2)? 02 04 O 1 0

A: A differential equation y'=f(x,y) represents the slope field of the curve y. at a point x0,y0 The…

Q: (a) Use a calculator to find e0.7(rounded to five decimal places). eº.7% (b) Estimate eº.7 by using…

A:

Q: Evaluate the integral: cos² (2x) sin (2x) dx Туре U U'

A: ∫01cos22xsin2xdx

Q: Using the coffee demand function, Q = 8.56-p-0.4ps +0.1Y, show that sugar is a complement for…

A:

Q: Identify u and dv for finding the integral using integration by parts. Do not integrate. " U= dv=dx…

A:

Q: Find the average value of f(x) = = √x² − 1,1 ≤ x ≤ 6. - X

A:

Q: 38. f(x) ex 1 + et

A: Since you have posted multipart question, i can do first three subparts as per our company…

Q: Using row operations, find the inverse of this matrix. 1 -2 -61 [6] 01 5 001

A:

Q: 5. Find the plane containing the line given by x(t)=4+3t, y(t) = -5+5t, and z(t)=3+8t that is…

A:

Q: Use partial fractions to find the area of the given region. 7 16x² y = y 3

A: Now area of the region f(x) from a to b formula Area=int_a^b f(x) dx

Q: 10 5 0 f(x) = vx - 5 5 10 15 20 25 30

A:

Q: Find the vectors T, N, and B at the given point. T = N = B || r(t) = (5 cos(t), 5 sin(t), 5…

A:

Q: Question 10 Use the graph to estimate the limit of the function shown in blue as x→0. -5 -4 -3 -2 -1…

A: Since you have posted multiple questions i can do first question as per our company guidelines,…

Q: Consider the function: f(x,y)=3xye 8x²-8xy + y²

A: We know that, a function f(x,y) has stationary points at that points where, the partial derivatives…

Q: 1. let y = x(x2+x)2  , Find y'   2. let f(x) = (5x)5 find f '(x)…

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Find an equation of the plane passing through the three points given P = (4, 2, 9), Q = (6, 7, 18),…

A: We have given three points as P = (4,2,9) Q = (6,7,18) R = (11,8,12)

Q: TT Find the Taylor series at x = for 7sin(x). (Make sure your answer has at least three terms.) 2

A:

Q: The Ninth Gate You arrive at the final gate, which leads into a building-like structure. You hope…

A: We need to find derivative and rearrange then in order.

Q: Compute the integral f/4 tan² (x) dx.

A:

Q: The owner of a skating rink rents the rink for parties at $440 if 20 or fewer skaters attend. For…

A:

Q: 5. Consider the following vectors in 3D: (1,2,3) & (-4,0,1). Determine a vector that is orthogonal…

A:

Q: What is the volume of the solid created when the region under the curve -4? (Solve using any y =…

A:

Q: 38. f(x) ex 1 + ex

A:

Q: Using the the derivative method power rule. How come the answer is 2t^-3? Instead of 2t^1?

A: Given: f=-1t2 We are required to find: The derivative of f

Q: Evaluate the integral. (Use C for the constant of integration.) [tan²(x) cos³(x) dx

A: let B=∫tan2xcos3xdx

Q: If v(t) = -t+2 and d(0) = -3, then d(t) = - + 2t-3. false Otrue

A:

Q: 3 What is f S₂² 1+1/2² dx ?

A:

Q: If y(t) = -² -1 and a(0) = 1, then d(t) = -2t + 1. false true

A:

Q: What is fxe- dx ? -x Oxe xee+C Ox²e-2x 2 + C X -xe-* — e * +C x² e-x 2 + C

A: Consider,

Q: Solve the formula for k 7k + ka a = f

A: Use multiplication rules

Q: 4 3 -3 +---)-(6) --- 00 0 12 0 A-1 = 120 A-21= 0 5 3 0 0 0 3 3 -3 -(6)-( 0 -1 0 1 2 -1 1 0 0 1 0 0 0…

A: ⇒A-I=43-3000120 ⇒A-2I=33-30-1012-1 ⇒A-4I=13-30-3012-3