X-2 if x s0 2. Draw a sketch of the graph of the function f(x) = - and evaluate the following limits: |x² -1 if x > 0 (a) lim f(x); (b) lim f(x); (c) lim f(x) (12)

Q: Find the derivative of the following functions using the increment method. *b. f(x) = 6- Зх 1 *а. f(...

A: Topic:- derivatives

Q: What is the area of the shaded region? y = y = -2x*

A: We will take difference of both curves to find the area using integration.

Q: The olid lies betcween planes perpendicular 4o the X=axis at x=0 and X=7,The Cross sections Perpendi...

A: Concept -we have a given two plane and perpendicular to x axis from x=0 to x=7 , We have to find sol...

Q: 4 1/2 - 3 Find k' (x) if k(x) = e Sorry, that's incorrect. Try again? K(x) = I

A:

Q: 5. A stone dropped in a pond sends out a circular ripple whose radius in- creases at a constant rate...

A:

Q: et dx Ve²x+49

A:

Q: +00 n! と+1 n=1

A:

Q: Given P = R³S°T°.5 + R0.5 S sin(2T), what is as O 2R³ ST0.5 +R-0.5 sin(2T) 3R ST0.5 + 0.5R-0.5 sin(2...

A: In this question,taking other part as constant and differentiate with respect to s. 

Q: find the solution of this differential equation: (x − 1)y′ = y + 2(x − 1)^3

A:

Q: Find the length of the curve y = x3/2 from x = 0 to x = 3.

A:

Q: Question VIn(2r +5x-1). Find the derivative of f(x) %3D Provide your answer below:

A:

Q: Graph of f The graph of the function f shown above has horizontal tangents at x = 2 and x = 5. Let g...

A:

Q: What is 3+4+5+8×9+3

A: Given query is to perform indicated operation.

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A:

Q: 2. S 1 dx | (2x + 1)3

A:

Q: 7. ex-4e-3 dx x- A 2 x + + С 2 + С et В х+2 е х + О D х - 2 е * + С

A:

Q: Evaluate the following limit. Use​ l'Hôpital's Rule when it is convenient and applicable lim x->0 ,...

A:

Q: find solution of this differential equation:  y′ tanx sin2y = sin^2 x + cos^2 y

A:

Q: Evaluate the indefinite integral. arctan dx

A:

Q: 2. The graphs of the functions f and g are shown below on the same axes. If h(x) (8(x))4 wh f(x³) 12

A:

Q: • Enter your ten data points in the chart below: Price ($/lbs) Quantity (Ibs) 3.467 10.000 3.555 9.8...

A:

Q: Using Integrating factors found by inspection (2y-3x)dx + xdy = 0

A:

Q: 3) (use DiSk Methad) Fnd the volur Solid genecated by revoluing the bay. the Sraphs Of the equatons ...

A: solution:-the region bounded byxy=3, y=1, y=4, and x=5 revolving about the line x=5using the Disk me...

Q: 3 x³ – 64x e. lim 5 .2 е. X + 2x

A: Topic:- limits

Q: Find the general term of the sequence, starting with n = 1. Determine whether the sequence converges...

A: Let's find. 

Q: A substance N1 decays with a half-life of 45 seconds to substance N2. N2 has a half-life of 5 minute...

A:

Q: 2.5. Give an example of a bounded function f and an increasing function a defined on [a, b] such tha...

A:

Q: 10. Seta x² dx A 2 е** + C с 1 + С B 3 e** + C D 1 + C 3.

A:

Q: *Find the equation/s of the tangent line/s to the curve y = x* - 6x and perpendicular to the line x-...

A: dydx =limh→0  f(x+h)-f(x)hdydx =limh→0   (x+h)4-6(x+h)-x4+6xhdydx =limh→0   x4+4x3h+6x2h2+4xh3+h4-6x...

Q: (1+,x£)u[ = (x)f I 'I %3D ,find f'(x). V(4x3 – 5x)2

A:

Q: +oo (-1)"+1 n=1

A: To show the convergence using alternating series test.

Q: Find the volume of the solid generated by revolving the shaded region about the given axis. About th...

A:

Q: 5. 3x² + x -1 x+2 A 3x2 + 5x + 9 In I x + 21+C 2. 3x2 - 5x + 9 In I x + 21+ C 2. B 3x2 + 5x + 9. + C...

A:

Q: The given curve is rotated about the y-axis. Find the area of the resulting surface. y = x2 - 1 - In...

A:

Q: Use the ALEKS calculator to evaluate each expressic Round your answers to the nearest thousandth. Do...

A: As we know that; The logarithmic properties; 1). logaxb=b·logax 2). logcab=logca-logcb   Given: (a)....

Q: Show that (sec x) = sec x tan x. Note: You may assume it is known that (sin x) = cos x and :(cos x) ...

A:

Q: X + 1 Find the equation/s of the tangent line/s to the curve y = where the tangent line is/are paral...

A:

Q: Find the absolute maximum and absolute minimum values of f(x) = x ln ,e). on

A:

Q: Give two examples of the situation with the solution clearly and in order Soperties of Bessel's func...

A:

Q: (a) Find the Taylor series of Ax) = usinge (b) Using the Taylor series found in part (a) find the ap...

A: Question - 1 Given function fx=11-xa=12 The Taylor series of a function f(x) at x=a is given by fx=f...

Q: Differential equation dy - 3x Initial conditions y=4 when x=9 1. dx %3D

A: Note: - “Since you have asked multiple questions, we will solve the first question for you. If you w...

Q: S Find the voleime of the solid generated by revolving the region baunded by the given lines Cnd cur...

A: Hint: Try Disk Method to find the volume.

Q: +o0 2" +1 3" +n n=1

A: Let's find. 

Q: 4. If two resistors are connected in parallel, then the total resistance R, measured in ohms is give...

A:

Q: A function f has a removable discontinuity at x = c if limf(x) exists by f is not continuous at x = ...

A: Here, the given function is: f(x)=x-2|x|-2 So, function is not defined at x=2,-2

Q: The graph of a derivative f' is shown to the right. Use the information in the graph to determine wh...

A:

Q: 2x – x3 1. Evaluate dx. (r – 1)²(x²+1). -

A: we want to find the value of the given integral I=∫2x-x3(x-1)2(x2+1) dx

Q: Use the differencean+1 – an to show that the given sequence {a, } is strictly increasing or strictly...

A: Difference = an+1 - an= (n+1)9(n+1)-8 - n9n -8=(n+1) 9n+9-8-n9n-8=n+19n+1-n9n-8=(9n-8)(n+1)-n(9n+1)(...

Q: 2. S dy 3ylny/9ln²y-25

A: To evaluate the integral: I=∫dy3y ln y9ln2y-25...(1)

Q: 1. Determine whether cach of the following sequences converges or diverges. If it converges, fin the...

A: Note: AS per our company's guidelines we are supposed to answer the first three sub-parts of the que...