1. If f(x) = 5x4 - 6x² + 4x - 2 find f'(x) and f'(2).

Q: √x-3 x-3+√√√x²-9 Evaluate lim

A: Given query is to find indicated limit.

Q: {CLO-1} Find the values of a and b such that the following function is continuous everywhere. ax²-a…

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Q: Given f(x) = x" ; n=1,2,3,....... Determine f(n)(x). (a) fm) (x)=n(n-1)(n-2)....∞ (b) sol…

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

Q: A Moving to another question will save this response. Question 11 {CLO-1} Find the values of a and b…

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Q: Use Integration by Parts (IBP) to evaluate the following integral. ² ln(r) + ³ + C 2² In(z)-2³ +C…

A: integration

Q: 6 Consider the three by three system of linear equations 2x + Y + + 2y + 2z 5z 12. We will solve…

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Q: explain using a graph of (x) = X³-6x, for 0≤x≤3 With Six sub intervals, what the Riemann sum…

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Q: Evaluate the following integrals: O •(Cartesian to Polar) Given the Cartesian coordinate, find FOUR…

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Q: 3. Find y' and the equation of the tangent line to the graph of In(ay) = y²-1 at (1,1). 11: 11:

A: We have to find y' and equation of tangent

Q: 2x y dA, D is the portion of the region between the circles of radius 2 and radius 5 centered at the…

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Q: Use a triple integral to find the volume of the solid bounded by the parabolic cylinder y = 62² and…

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Q: Find the general solution of the following linear first-order ODE (1-x²)y' +2y-x=2

A: We need to solve D.E.

Q: Find the general equation of the conic with the given properties. 51 59 1. A parabola with directrix…

A: Given: A parabola with directrix y=-5132 and one endpoint of the latus rectum at -18, -5932

Q: (31) Use Newton's Method to make the second approximation x2 to the solution of 2e* = ex. Take x₁ =…

A: We have to use Newton's Method to make the second approximation.

Q: 10dz 4z³-4z²+5z

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Q: Əw at = xysin(z2), x= s-t, y=s2, z t². Use the Chain Rule to find .

A: We know that derivatives of d(xn)/dx = nxn-1. And d(sinx)/dx = cosx  Here i attached the solution of…

Q: 5s + 4 83 2t5t³ Option 4 None of the Choices 2t + 5t³ Option 3 Option 1 5t + 2t³ 5t - 2t³ Option 2

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Q: 10. Determine the surface area of the part of z = xy that lies in the cylinder given by x² + y² = 1.

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: The proper way to evaluate f (3 + h) for the function f(x) = −4x² + 3x − 1 is Of(3+h)=(−4(3)² + 3(3)…

A: We can answer the question as below.

Q: Is it possible to solve all the points with Finding Domain and Range 1) y sin x 2) y = cos x J= tan…

A: Solution is given below

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: 2 3s + 9 Option 4 Option 2 -3t e 2 3 e 23 c -34 3 None of the choices 3 -34 2 Option 1 e

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Q: M8 ทะเ (23 - +3 1 k +4

A: ∑k=1∞ 1k+3-1k+4

Q: Determine the intervals on which the graph of y = f(x) is concave up or concave down, and find the…

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Q: 4. Use the Fundamental Theorem to evaluate (x³ - 6x)dx . (Your answer must include the…

A: Use the integral of polynomial.

Q: etermine the derivative of f(x) = a. f'(x) = -x_ 7 cos x − tan² x− 1 (secx+7)² b. ƒ'(x) = − µ* _ 7…

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Q: Given the polar coordinates (1,7π/8) determine (x,y). What is x=______. (round to 3 decimal)

A: In this question, we need to find the rectangular coordinates (x, y) from the given polar…

Q: use the graph of the function √²³ (x³²-6x) dx to explain the geometric meaning of the value of the…

A: Given function ∫03 (x3-6x) dx This below image is the graph of the function

Q: Find the point on the plane 5x + 4y + z = 11 that is nearest the origin. What are the values of x,…

A: First we find the distance(d) between a point (x,y,z) on the plane and the origin .Then form a…

Q: S x²-x+1 x² + 2x + 2 2 -dx

A: We need to evaluate integral.

Q: Find an equation of the sphere with points P such that the distance from P to A(-2, 4, 4) is twice…

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Q: 8. 9. 10.¹₁²(x² (2-y)dy dx π/4 /²x cos y dz dx dy + y² + z²) dx dz dy

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Q: 2) lim f(x) if f(x) = {x²43) X2² fx²-9, x2 x-2 F(x) X 2.75 2.5 2.1 2.01 2.001 X 1.5 1.75 1.9 1.99…

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Q: What is the area of the region bounded by the graph of the function below? 2x + y = 8, x-axis and…

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Q: General solution of (ylny − e¯xy)dx + (² + xlny) dy = 0

A: Let's solve given diffrential equation.

Q: Find the area of the region bounded by the curves below. Sketch its graph and shade the region. 1.…

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Q: n³r" Find the radius of convergence for the series 1 3⁰ OR= =/3 OR=1 OR=3 OR=1/ R = ∞

A: According to our guidelines we can answer only one question or three subparts of a question. Other…

Q: Evaluate the triple integral ryd xydV where E is the solid tetrahedon with vertices (0,0,0), (10, 0,…

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Q: Find the particular solution (D² + 4D + 4) y = 0 when x = 0, y = 1 and y' = -1 What is the general…

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Q: Given z *- Find Z*** www.xy. www Option 1 Zxx = -2x³ Zxx = -2x-3 Option 3 Zxx = 2x 3 Option 2 none…

A: Given

Q: Evaluate the triple integral [ 2³ dV, where E is the solid tetrahedron with vertices (0,0,0),…

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Q: 4. Find the components of the vector with the opposite direction to that of the vector from M(2,3,5)…

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Q: Evaluate the triple integral where E is the solid: 0≤z≤ 10, 0≤ y ≤z, 0≤x≤y. Izydv

A: Solution:

Q: Obtain the output for t = 1.22, for the differential equation 2y"(t) + 27y(t) = et + et :y(0) = 0,…

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Q: Determine the constant a so that the vector V = (x+3y)i + (y-2z)j + (x+az)k is solenoidal.

A: Follow the procedure given below.

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

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Q: Consider the functions z = 7 e* In y, x = In (u cos v), and y = u sin v. ex əz dz (a) Express and as…

A: This question can be solved by the concept of partial derivatives.

Q: Find x²-x-12 lim x--3 x2 + 8x + 15

A: We have to find limit of given function

Q: {CLO-3} The function f(x)=2x4-4x² has a local maximum at x=-1; and a local minimum at x=0 has no…

A: Topic:- application of derivatives

Q: Find the critical points of f(x) = x³ - 21x² + 144x and use the Second Derivative Test (if possible)…

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