Complete the table to find the derivative of the function. Original Function Rewrite 4 y = X 3+4 Differentiate X Simplify

Q: 3) Suppose 2X z = xe cos 3y, find all the first and all the second derivatives.

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Q: What is the coefficient of the second term in a binomial that is raised to the sixth power?

A: Given.

Q: Tutorial Exercise Calculate two iterations of Newton's Method to approximate a zero of the function…

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Q: Find the nth Maclaurin polynomial for the function. f(x) = ex, n=5

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Q: Find the derivative of f(x) = a√². f'(x) = 9.

A: We know, d/dx (xn)= nx(n-1), for any real number n.

Q: 2. Find the value of 1 3x + 13 x² + 4x +3 dx

A: We can you valve the given definite integral by using the partial fraction method.

Q: 1. [(5x (5x - 3)100 dx 2. (x - 3)¹/4 dx 5 3. 3. / ( x ² + ² ) ( ²2 2²³ + x) ² da 2) dx

A: 1) Given ∫5x-3100 dx Substitute   u=5x-3                  du=5 dx    ⇒ dx=du5 ∫5x-3100 dx = 15∫u100…

Q: 5. A function u(x, y) is defined by u2³-3xy². (a) Show that u is harmonic, i.e. it satisfies…

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Q: (B) What function f(t) has Laplace transform: f(s)= s² + 1 s(s+s-12) 12

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A: Given , Initial population P=484,000 rate r =9% time t=17 year

Q: If z₁ = 5-i, z₂ = 1-2¡ then evaluate 32₂ +22₁-5- z, 2z, -3z₂ +3-i

A: Use complex number concept

Q: 4. f(x, y) = 5xy - 7x² - y² + 3x − 6y + 2 5. f(x, y) = (xy − 1)² 6. f(x, y) = (2x - 3y)³

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

A: Topic:- limits

Q: 2. f(-7sinx + 3cosx)dx (-7sin 3. √(3x − 2 + sin x) dx TE 4. (3 sec² x + 4 csc² x) dx

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Q: 2. If Ac B then BCA.

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Q: Find the solution of the given initial value problem. ty' + 2y = sint, y() = 9, t>0 y

A: y' +2t y =sin ttEquation is of Bernouli's form:P(t)=2tIntegrating Factor:I.F.=e∫ P(t) dt     =e∫2t…

Q: Suppose that f(x) is a function with f(85) = 49 and f'(85)= 3. Estimate f(80). f(80) =

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Q: Given the number or numbers where the function is discontinuous. Is the discontinuity removable?…

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Q: Suppose that 5 J of work is needed to stretch a spring from its natural length of 24 cm to a length…

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Q: Q1/ Find the derivative of the following functions: where x>0,x #1 a- y = x** x√√2x+1 b- y = exsin…

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Q: π Determine the Taylor series for f(x) = sin x about x == 3

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Q: y=ex5

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Q: Solve the general solution of the equations in items 3-4. 2 (2x² + y²) dx - xydy = 0 C Oy-1=x-3+C…

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

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Q: Joseph completed the two problems, asking him to explain if there is enough information to prove the…

A: Given.

Q: Q5: (A): Finding a curve whose slope at the point (x, y)is 3x² if the curve is required to pass…

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Q: Problem 2. Find an equation for the tangent line to the curve y = 2x² + x3 at x = 4. You must use…

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Q: (B) Use Tabular integration to evaluate the following: - f(t³-4t² + 5t+32)sin(t)dt

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. 5…

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

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Q: Find the arc length of the curve x = Length = -2y³/2 from y = 0 to y = 10.

A: See the details solution in below

Q: For each of the questions below, indicate if the statement is true (T) or false (F). (a) Any…

A: answer  is next step . as per guideline i can only answer 3 question .

Q: Q2: (A) Show that if y=csc(u), then dy -csc(u) cot(u) du dx

A: I have stated the used formula in the solution

Q: The arc length of y=In(cos x), 0<x<• is 3 ○A In (√2-1) A. ○ B. In (1+√3) C. In (2+√√3) D. In…

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Q: For the function f(x,y)= x + 4y 3 4 x +y find f, fy, f(5,-5), and f,(1,3).

A: For the function fx, y=x2+4y3x3+y4, to find fx, fy, fx5, -5, and fy1, 3.

Q: The height (feet) of an object launched in the air t seconds after launch is given by s= - 16t²…

A: see below the answer with explanation

Q: 2 n (2k + n)2 k=2

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

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A: Solution

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Q: PART I. Calculating First Order Partial Derivatives 1. f(x, y) = 2x² - 3y - 4 3. f(x, y) = (x² -…

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Q: PLEASE ANSWER:  Find the number in the interval [−1, 1] such that the sum of the number and its…

A: To find the number in the interval [-1,1] satisfying the given conditions.

Q: -2, if x < -1 f(x) = (x + 1, if x ≥ −1

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Q: Find the arc length of the curve x = Length = -2y³/2 from y = 0 to y = 10.

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Q: Q1/ Without using L'Hopital rule, find the following limit. x²-x-2 lim 4x²+4x

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Q: 2. Find the coordinates of the y-intercept of the plane (x, y, z)=(4,6,5) +s(2,3,1) + t(3,6,12)

A: To find out the coordinate of y-intercept.

Q: [1 0 1. Let A = = (i) AB (ii) BA (iii)Is AB=BA? 41 2 -3 4 -5 -1 1 2 VY and B = 23 -5 0 6-2 [-1 -3]…

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Q: 5. 6. tan x dx \cos x (1/2-√√x) dx HIM

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Q: Differentiate r(t)=

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