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Q: Differentiate. f(x) = x2 sin(x)

A: To determine the derivative of the function.

Q: Calculus Question

A: Given,

Q: Express the given quantity as a single logarithm In(x 2)7 In x In(x23x 2)2 2

A: Make the coefficients into exponent. And they will multiply with the existing exponents.

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A: From the equation for x, write t in terms of x.

Q: A rectangular tank with a square base, an open top, and a volume of 6912 ft^2 is to be constructed o...

A: Given tank is open at top.So, the surface area is,

Q: see attachment

A: Since tan x = 1/2 and tan x=opposite/adjacent Let opposite = -1 [because of third quadrant]adjacent ...

Q: if x1 Let f(x) mx b if x > 1 Find the values of m and 6 that make f(x) differentiable. т

A: Given :

Q: indefinite integral of (7 + ex) dx

A: Consider the given indefinite integral:

Q: Differentiate the function F(t) = (ln t)2 sin t

A: Given function is,

Q: Differentiate. y = (4-sec x)/tan x

A: Distribute tan x.1/tanx= cot x and secx/tanx= cscx

Q: f(x)=(2x^3)-(15x^2)-36x+7 on the interval [-6,9]. Find the average or mean slope on this interval. B...

A: Click to see the answer

Q: Solve the equation for x. Need full answer. 272x+1=1/3

A: Given:

Q: Г. 5 1, г)ах — 9, g(x)dx 8 Compute: -[о g(x)dx b.) == 5 3f(х)dx %— с.) .5 f(x)dx d.) 2 "/Г 5 [f(x)-g...

A: Given,

Q: I am very confused about this chapter and specifically on how the homework is breaking the problems ...

A: Given sequence is

Q: Systems of Linear Equations and Matrices 292 CHAPTER 6 6.3 Exercises of Use systems of equations to ...

A: You have asked two questions in a single post. I will address the first one. Please post the other q...

Q: Analytically, what is the slsmt symptote of the following function. Please shoiws alll math.

A: Given function is

Q: An arithmetic sequence is defined by Un=11n-7. a find U1 and d. b find the 37th term. c what is the ...

A: (a)Given:

Q: see attachment

A: Click to see the answer

Q: if sin(0)=-7/25 with 0 quadrant IV, what is cos(0)?

A: Given

Q: Find positive numbers x and y satisfying the equation xy=15 such that the sum 3x+y is as small as po...

A: Click to see the answer

Q: I am studying for a precalc exam. Could you explain how to find the inverse of a function such as: ...

A: Plug g(x)=y , then switch x and y.

Q: Find the following indefinite integrals. X dx= Vx6 +C

A: Given,

Q: Problem 2: For the following statements, say whether they are true or false. If true, provide a brie...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: Can you help with this problem step by step?

A: As per norms, the first three questions (of the multi-part problem) are answered. To identify the cr...

Q: f(x)=(4x^2)/[(x^2)−4]. Calculate the first derivative of f. Find the critical numbers of f, where i...

A: The given function is,

Q: Sketuh fCx)= x-DA2x1) ( 12X21 7xt1 X-intercept Doman: 10 Y-inteicept 10 Slant Asymptote: Vemcal Asym...

A: The given function is:

Q: Find the area of the region enclosed by one loop of the curve. r=sin(8theta)

A: Draw the given curve as shown below.

Q: lo eTTIoprvars ruc, -too 42 3r (c) Use the substitution rule to show that lim0 f(x) = lim^0+ f() and...

A: Given

Q: For what value of k will y=2x^2+kx-9 have a minum at x=3?

A: The given equation is,

Q: A corporation recently sold zero-coupon $200 bonds maturing in 3 years with an annual yield of 12%. ...

A: The price is the present value of $200, 3 years from now at the stated interest rate.

Q: Calculate dy/dx Simplify your answer. y = x3(8 − x2) dy/dx=

A: Product rule:

Q: see attachment

A: Simplify the argument to find the exact value

Q: Evaluate the integral dx/2sqr(x+3)+x

A: Given that

Q: see attachment

A: Click to see the answer

Q: Use a graph of to estimate the maximum and minimum values. Then find the exact values. Estimate th...

A: Please see the graph on white board. The maxima is infinity and minima is 0.

Q: Evaluate h'(6) where h(x) f(x) g(x) given the following. f(6) 5 f'(6)2.5 g(6) 2 g'(6) 1 h'(x)

A: The function h(x) is given by,

Q: Find the area of the region bounded by x = y^2 - 2, y = ln x, y = -1, and y = 1. Sketch the region.

A: We graph the functions first. We need to find the area of the shaded region.y=lnx => x= e^y

Q: Determine the equation of the tangent line to the given path at the specified value of t. (Enter you...

A: Given:Determine the equation of the tangent line to the given path at the specified value of t.

Q: 3.4 Can you show me the steps to solve the problem? Directions: Find the limit or show that it does ...

A: The given limit is,

Q: let f(x)=1/2ln(1+x/1-x). compute the inverse function f-1 (x) and find its domain and range.

A: Find the inverse of the function and find its domain and range

Q: Need help and exlination on solving this problem

A: Click to see the answer

Q: Evaluate the integral by changing to spherical coordinates. 2 - x2 -y2 16 x2 4 yz dz dy dx 0 10 x2 y...

A: The integral is given by,

Q: I am studying for a precalculus exam and I am stuck on this problem and would like help. Question...

A: Given equation is

Q: 7. According to a simplified economic model, the purchasing power of 1 dollar in the 2000t is equal ...

A: 2000+t=2020So, 20 years.

Q: The marketing division of a large firm has found that it can model the sales generated by an adverti...

A: From the given information, it is observed that the aim is to find the ds/dx at the point x = 16.

Q: find f'(x) of (((3x^2+1)e^x^2)/(2x+1)^5)^5 using logaithmic differentiation.

A: The given function is,

Q: find the critical numbers of the function

A: Firstly, we find h'(t) for given function h(t)

Q: Find the absolute maximum and the absolute minimum values of f on the given interval.

A: Calculate the derivative and equate it to zero to get the critical points,

Q: For the composite function, identify an inside function and an outside function and write the deriva...

A: Part (a): Let’s consider two function g(x) = 9x5 and h(x) = 3x2 + 2 (g o h) (x) = g(h(x)) = g (3x2 +...

Q: f(x+h)-f(x) Simplify the difference quotient for the given function. f(x) 4x2-5x+5

A: First find f(x+h).Replace x by x+h in f(x)=4x^2-5x+5