Find the average rate of change of the function over the given interval. f(t) = 13+ sint a. 0, 플] п Зл b. 2'2 TU a. The average rate of change over (Type an exact answer, using as needed.) IN EIN

Q: {CLO-3} Find the absolute minimum value of the function f(x)=x²-3x²-24x +5 on the closed interval […

A: This question can be solved using the concept of absolute maximum and minimum.

Q: Find the volume V(S) of the solid S generated by revolving about the x-axis the region R bounded by…

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Q: Find all the relative extreme values in the domain of y = tan(x)

A: Find all the relative extreme values in the domain of y = tan(x)

Q: Q2/Test whether the differential equations are exact and solve those that are. (Answer only two) -y²…

A: We have to solve given differential equation.

Q: 5x² Find all critical points of the function f(x) = 7x²–2x+6* (Use symbolic notation and fractions…

A: For critical points , f'(x) =0.

Q: Click to see additional instructions For the demand function f(x) = (x-4)² and the supply function…

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Q: If x + y = 2 , x” + y” = 3 , . Find the value of x(4) + y(4) a. 6.65 c. 8.5 b. 6.55 d. 8.75

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Q: (a) Find the general solution of the differential equation d²y dx² +9y = x² + x + 1.

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Q: The solution to the differential equation (DE) y''(x) + c2y(x) = 0 is/are: a. y = esx b. y = a0 +…

A: The given differential equation is;  y''(x) + c2y(x) = 0

Q: Syy-mat sama dy ³

A: Follow the procedure given below.

Q: Find the derivative of y with respect to x. y= (x8 Inx) 5

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Q: Evaluate the triple integral a dV where E is the solid bounded by the paraboloid a = 10y² + 102² and…

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Q: The area between the curve y = 1/x, the y-axis and the lines y=1 and y=2 is rotated about the…

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Q: SUBJECT: DIFFERENTIAL CALCULUS NOTE: Make the solution detailed and clear in a sheet of paper.…

A: Topic:- application of derivatives  Note:- as per our guideline if more than one question uploaded…

Q: Evaluate the following integrals: 4x 6. ²x3x²y²dy dx -TT/3 7. p² sin 0 de dp Jπ/6 S3

A: The integration of the integral is  6) 3x2y2 7) (row) 2sin(theta).

Q: Numbers 4,5,6 please

A: Let's solve  given integration.

Q: Consider the function 2r²-9r-18 f(r) r²-r-2 (a) Sketch the curve y = f(r). (b) Find the area of the…

A: Here we have to find the area under the curve

Q: 1. f cos³ 3x sin¹ 3x dx 2. fcsc4 5x cot4 5x dx 3. ƒ cos³ xdx from a = 0 to b = 2

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Q: nd the area of the plane region bounded by y=sin x, y=ex, x T 2 T D 2-2 s.u. D 2 S.U. 2+1 s.u. T 2-1…

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Q: find the distance from the point P (2,1,1) to the lins x+1 y-1 Z-3 L: 6 -2 -3 = =

A: To find the distance from the point to the line.

Q: For numbers consider a plane bounded by the curve y = 4-x² and the x-axis. Which of the following…

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Q: A. Find the general equation of the conic with the given properties. 1. A parabola with directrix…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Evaluate the following integrals: O • (Cartesian to Polar) Civen the cartesian coordinate, find of…

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Q: Test the convergence of the following: n 3n+1 1- an 3n-1

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Q: In(x²y)- ez-tan"¹ z. Assuming that z is a differentiable function of x and y. Let F(x,y,z) Find F.…

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Q: X1 (-1, 2) & (-3,0) Y₁ ; X₂ = m m 11 -C Y2 =

A: Solution of given question is written in below steps.

Q: 7. Determine the volume of the region that lies under the sphere x² + y² +2²=9, above the plane z =…

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Q: Find the volume of the wedge-shaped region (Figure 1) contained in the cylinder x² + y² =25 and…

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Q: {CLO-2} Find the linear approximation, L(x), to f(x) at x = xo . f(x)=√10x+9, x = 0 O 10 L(x)=x+3…

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Q: Q1): Prove that: A square matrix B has inverse if and only determinant of B is not equal zero.

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Q: The critical number(s), if any, of the function f(x) = (x²-3x+2) is (are):

A: critical points of fx=x2-3x+2-13

Q: Find if dy dx y = (cos x) * O (cos x) * (-sin x) O (sin x) * (In cos x - x tan x) O (sin x)* (In cos…

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Q: Given the function y = 8e-²x² + 7 sec² 5x – 4 ln x³, find y'. Solution: y' = 4(3)x² x³3 +8(−4x)e-²x²…

A: We will find the y' of the given function in the following step.

Q: A horse tied to a post with twenty foot loop. What is the longest path that the horse can walk? a.…

A: Here we have to find the circumference of a circle.

Q: Q4) Find the largest eigen value for the matrix A= 54 with x (0)=(7/17 1)

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Q: Find the value of the following implicit derivative tan y-sec x=5 find...y'

A: Given problem :- Find the value of the following implicit derivative   tan(y)-sec(x) = 5 find   y'

Q: Use Taylor's formula for f(x,y) at the origin to find quadratic and cubic approximations of f near…

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Q: Find at least 5 distinct rational points on the unit circle in the first quadrant of the plane.

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Q: Find the mass of the rectangular prism 0≤x≤2, 0≤ y ≤2, 0≤z <3, with density function p(x, y, z) = =…

A: Mass = Density * Volume

Q: 10 5-2 sin 8 a. find the eccentricity and identify the type of conic; b. write an equation of the…

A: This is a problem related to polar function. Based on the general formula and concept we will answer…

Q: 7. The particular solution of (D³ + 2 D²-5D-6)y = 0, when x = 0, y = 0, y = 0, y" = 1

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Q: -5e-cos2t O Option 4 5e-t sin 2t O Option 2 5e¹ cos2t O Option 3 5e sin 2t O Option 1

A: Topic:- application of derivatives and integration

Q: Find all the relative extreme values in the domain of y = 4x2 - 3x

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Q: S0³ (0+2) de -3

A: ∫θ-3θ+22dθ

Q: How to solve dx = 2dy = -2dz.

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Q: gh (2,-5), parallel to y= 2x+4

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Q: Find the value of the following mplicit derivative tan y-sec x=5 find...y'

A: Given query is to find the derivative of the expression.

Q: 2.) given this trigher ODE, use the reduction of HODE via of systems ODE and find the general non…

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Q: Find the Taylor series for about f(x) = x³ + x² + x + 1 a = 1

A: As we know the Taylor series; fx=fa+f'a1!x-a+f''a2!x-a2+f'''a3!x-a3+.... Where center at x=a.…

Q: Find all the local maxima, local minima, and saddle points of the function. f(x,y)=-3x²-3xy-8y²…

A: This is a problem related to maxima and minima of the function. Based on the general formula and…