Find the values of xER for which the function given below is both defined and continuous. f(x)= In (x-9) The function f(x) is both defined and continuous on (Type your answer in interval notation.)

Q: Find the center of mass of a lamina as pictured below, with inner radius 3 and outer radius 5, with…

A: Given problem:-

Q: 12) Find the equation of the line tangent to g(x) = (3x + 11)ex-4 at x = 4.

A: ddxuv=vddxu-uddxvv2

Q: -15 Evaluate the integral: -dz x²√²+64 (A) Which trig substitution is correct for this integral? 0x…

A:

Q: If a snowball melts so that its surface area decreases at a rate of 3 cm2/min, find the rate at…

A:

Q: Problem 1: A force of 500 dynes stretches a spring from its natural length of 20 cm to a length of…

A: Concept: Work done by integration: W=∫x=abf(x)dx Where W represents work Force is represented as a…

Q: The value of a is Blank 1. The value of b is Blank 2. Let R be the region enclosed by the curves y =…

A:

Q: 1. f(x) = 10 2. f(x) = 3 − 4x 1 2 3. f(x) = x² - 9x 2 4. f(x) = x² + 5x + 4 5. f(x) = 2 + 7x - 2x²

A: See the details solution in below

Q: Q2/ Compute the following integral: 3 x √x - 4 dx

A:

Q: se the formula to find the derivative of below functions. 5x²-7x+2 2³-9 (1) ƒ(x) = ( 31⁄4 + x) .· (2…

A:

Q: 5. If A is (8, -7) and B is (5, 16), find a unit vector in the same direction as AB.

A:

Q: Applications

A:

Q: Find the linear approximation at x = 0 to Write your answer in the form y = Ax + B.

A:

Q: 2 ind the arc length for f(x) = 6-2 x² over the interval [0, 2].

A:

Q: Given the function  y = 5 arcsin(x),  find  y'.

A:

Q: Sketch the graph of a function f that is continuous on [1, 5] and has the given properties. absolute…

A: Given problem:- Sketch the graph of a function f that is continuous on [1, 5] and has the given…

Q: Find the derivative of the function. g(x) = ((7x^2-4)/(4x+7)^-2

A: We have to find the derivative

Q: Let g(x) be the inverse function to the differentiable function f(x). If f(0) = 1 and f'(0) = 9,…

A:

Q: (2 fi = f(x²+xyz, y² +22= Prove that (y²-2x) ou 2ZX) then ne (²h-x) he 18

A: Concept: Partial derivative : The partial derivative is similar to the normal derivative except in…

Q: Show that the Fourier series of is: 2 ƒ (a) = (1/2 + 1). - Σ n=1,3,5,00 1 1 Hence find the sum of…

A:

Q: 6. S²2 (+1/12 - √x) dx

A:

Q: X hat is the value of lima f(a)-aƒ(x)? r-a

A: Topic:- limits

Q: Given the differential equation xy³dx + (x²y² + 1) dy = 0, What is SN dx ?

A: We are asked to find the δNδx

Q: 1. Solve the homogenous linear equation given below. xydx − (x + 2y)²dy = 0 F + ln (x+y) :) + 4 lny…

A: In this question we have to solve the homogenous linear equation.

Q: 8. a. Using the vectors x = (3, 3, 1) and y = (-−1, 2, -3), verify that the following formula is…

A:

Q: Jse the definition of derivative to find f'(x) where f(x)=√x

A: Given,  f(x)=x

Q: 11. A dangerous toxic pollutant has been accidentally spilled in a lake. t The speed of water…

A: Use algebraic concept

Q: 3e-20 + 2x 3.y" + 6y + 8y = 3e-2x

A: Here we have to solve the differential equation.

Q: ? Question Calculate * (z3y + 1) y2 dy dr.

A:

Q: 3 S² 2 (3x+1) dx x-1

A:

Q: What is the solution of 3x2 + 6xy2 + (6x2y + 4y2 ) y' = 0

A:

Q: 8. · √(x) √₁² 1 9. J 5x + 1 dx 10. S 3x +9 (x) √√x² - 1 dx dx

A:

Q: The total revenue (in hundreds of dollars) from the sale of x spas and y solar heaters is…

A: Concept: Rxx, Ryy, Rxy, are the double partial derivative of x and y Maximum condition:…

Q: The figure shows f, f', and f". Determine which is which. 2 y 0 -2 1

A: In this question we have to determine which is f, f' and f''.

Q: W1 3. Let w = , v = (m₂). Referring to the image below, show that the area of the parallelo- W2 gram…

A: We need to solve for area. As per Bartleby's guidelines we can solve one question from multiple…

Q: . Solve the given equation by simple substitution. (2x + y)² dx - 2dy = 0 O x + Arc tan 2x+y = C 2 O…

A:

Q: 1. A plane is defined by the equation x - 7y - 18z = 0. a. What is a normal vector to this plane? b.…

A:

Q: 5. y + 4y= sin x + 3 cos x Ans: y = C₁+C₂ cos 2x + C3 sin 2x + sin x x-co COS X

A: To solve the given differential equation.y'''+4y'=sin x+3 cos x

Q: 5. For items 1-2, identify the substitution equations and solve the solution for each. (x - 2y + 5)…

A:

Q: Q1/Without using L'Hopital rule, find the following limit. lim

A: We can solve the question as below and as per the asked method.

Q: Calculate the double integral. 3ху2 11 3xV²_ DA, R = {(x, y) 10 ≤ x ≤ 3, -2 ≤ y ≤ 2} d R + 1

A:

Q: Find the radius of convergence of the power series. (If you need to use oo or -00, enter INFINITY or…

A:

Q: A line segment has (x₁, y₁) as one endpoint and (xm, Ym) as its midpoint. Find the other endpoint…

A:

Q: √y² +9 dy 4 X using reciprocal substitution

A:

Q: Ise the binomial series to find the Maclaurin series for the function. f(x) = √√1+x DO 1 x) = 1 + x…

A: To find the series expansion of following

Q: Find a tight upper bound for the approximation to * cos(z) cos(x) Note that the second derivative of…

A: Concept: Midpoint rule: Assume f(x) is a continuous function on [a,b]. Let n be a positive integer…

Q: dy dr = cos(²) +

A:

Q: Q3/ solve the differential equation below: 1. ²-3x+2y=0 (Complementary Function)

A: topic- differential equations

Q: . A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

A: . A thermometer is taken from an inside room to the outside ,where the air temperature is 5° F.…

Q: Find the nth Taylor polynomial for the function, centered at c. 1 f(x) n = 4, c = 2 +2² P4(x) = = =

A:

Q: Match the following functions with the appropriate cross-section: I) z = (y²-1) cos(x) II) z=(x²-1)…

A: