5. Verify the three conditions of the hypothesis of Rolle's theorem are satisfied by the given function and find a suitable value for c that satisfies the conclusion of Rolle's theorem: f(x) = -x³-x+ 2; [1, 2]

Q: Find the Jacobian of the transformation z = 4u – 6v, y = u² − 2v

A: The objective of the question is determine the jacobian transformation.

Q: Solve the given by simple substitution (2x + y)² dx - 2dy = 0

A:

Q: dy 2.L/+R/+y=0 dx2 dx

A: Homogeneous Differential equation with constant coefficients.

Q: Q.14) A sequence {()L a) converge to 3 b) diverge lecreasing

A: According to the guidelines, we are answering first question. Please repost the remaining.…

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

A:

Q: 8+2x-x² x-4 8 x=4 than f(x) is continuous at x = 4. book Ask my instructor I T - |0| √i 5 Vi 1, 3…

A:

Q: Suppose that f(x) is differentiable for x > 0, y = 2x + 1 is the tangent line to the graph of f at x…

A:

Q: Compute f(c+h)-f(c) at the indicated point. f(x) = 6x²; c=3 f(c+h)-f(c)= at c=3. (Type an expression…

A:

Q: x-1 f(x) = x= 1 at (2₁²) x+1

A: The objective of the question is determine the slope of the line tangent.

Q: Q.2) If a-1.a +3,a+12 are consecutive terms in geometric series, then the value of a is: 이쁨 이렇

A:

Q: (d) Any local minimum or local maximum of a function f must occur at a critical point of f. True…

A:

Q: Solve the system (2+i) z1+iz2 = 1-i 12321-322 = -1-7i

A: Given: Now,            2+iz1+iz2=1-ii23z1-3z2=-1-7iSubstitute…

Q: (3x-1) dx 2x²+2x+3

A:

Q: Let g(x) be the inverse function to the differentiable function f(x). If ƒ(0) = 1 and f'(0) = 5,…

A:

Q: Find the surface area generated by revolving the curve x=y³²-y about the y-axis for 1≤ys 3/2 1/2 3

A: Solve the following

Q: 4. · [ (8x − 3) (4x² – 3x) ³ da x J dx - 4x² x S dx 3 - 5x² 5. 6.

A:

Q: Figure out the following limits. (No L'Hopital Rule) 2x sin x-a b. lim a. lim 1-0 sinr - tan a -a…

A: Given

Q: y = 3-x²

A:

Q: 370 0 3sin²2x dx

A:

Q: a. Find the Taylor polynomial of 6th order at a=- 2 b. Find error at x = π. X c. Graph the original…

A: To solve the following problem

Q: Show that the points form the vertices of the polygon. right triangle: (−4, 5), (0, 7), (2, 3)…

A: The given points are -4,5, 0,7, 2,3

Q: The answer is Blank 1. Blank 1 Add your answer Let R be the region enclosed by the curves y = x³ and…

A:

Q: 1. For what value of k if the line 6y +(2k-1)x= 12 perpendicular to the line 3y - 2x = 6

A: A line perpendicular to another has a slope that is the negative reciprocal of the slope of the…

Q: 2 Find the volume of the parallelepiped whose edges are represented by A =î - 13ĵ+ 4k, B = 3î+ 2j-7k…

A:

Q: Q1:- A. Solve the following differential equatic 1. dx = (1 + y²)ex

A:

Q: dy dx = (1 + y²)ex dx

A: As per the instruction, we will be answering the first question. For (1),      y'…

Q: Let R be the region enclosed by the curves y = x³ and y = 2x². If we revolve R about the line y =…

A:

Q: Find [₁₂² r²dA where R = {(x, y) | 36x² +9y² ≤ 324} R 81T X

A:

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: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

A:

Q: et dx 2 S² teed x 3

A:

Q: Compute Ay and dy for the given values of x and dx = Ax. (Round your answers to three decimal…

A:

Q: Evaluation. 1. J (sinu + u) du 2. (1-cosv) dv Integrate each of the following. Show complete…

A:

Q: Question # 01 Solve the following Differential equation using variable separation method. dy 1)…

A: Concept: Variable separable method: Any differential equation in which variables may be separated is…

Q: B. Solve the following differential Equations y" - y' = 4x³ + 6x²

A: The given differential equation is  y'''-y'=4x3+6x2

Q: 3rc Som sin ² (2) ves" (4) dix

A: Wallis Integral formula :

Q: A box, with a square base is to have a volume of V = 360 cubic inches. The cost for the materials of…

A:

Q: Let R be the region enclosed by the curves y = x³ and y = 2x². The area of R using vertical element…

A:

Q: 2 (2x² + y²) dx - xydy = 0 X2 O = C y² +4x²2 ○ In x + In (²4²) = C Oy - 1 = x - 3+ C .2 X O = C…

A:

Q: Let X be the 3 x 3 matrix such that left-multiplication by X has the same effect as applying the…

A: In this question we have to find the (1, 2) entry of x.

Q: - 3x Find the derivative of y with respect to x if y = e

A:

Q: The answer is Blank 1. Blank 1 Add your answer Let R be the region enclosed by the curves y = x³ and…

A:

Q: Q.23) cos Q.24) cos(sin ¹x) = 24 sin11x) √1-1 d)√1-x² b) (sinx+1)+c 11

A:

Q: Complete the table to find the derivative of the function. Original Function Rewrite 4 y = X 3+4…

A:

Q: The function (f) is defined by: F(x)=x² if xe[-^;^] (i) Give the graphical representation of the…

A: Disclaimer: “Since you have posted a question with multiple sub-parts, we will solve the first three…

Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) = 3 (1+x) f(x) Σ = n=0

A:

Q: The function f(x) = = √x 2+√√4x is. increasing on its natural domain increasing on (2, 3) and…

A:

Q: Suppose that the graph of the velocity function of a particle is as shown in the figure, where t is…

A:

Q: Determine if there are any inflexions on the graph given by y=2x4-3x³+ x²+6. Proof they are points…

A: The given function y=2x4-3x3+x2+6

Q: (b) Find the general solution of: əz = yx² - xy Əx Given z = y when x = 1, determine the particular…

A: