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Q: Use the definition of the derivative (don't be tempted to take shortcuts!) to find the derivative of...

A: solution:-f(x)=4-9x6+5xf'(x)=6+5xddx4-9x-4-9xddx6+5x6+5x2       =6+5x-9-4-9x56+5x2       =-54-45x-20...

Q: 2 (a) Find the particular solution of the following equation satisfying the given initial conditions...

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Q: A cylindrical water tank 4 meters high with a radius of 2 meters is buried so that the top of the ta...

A: First of all, consider water thickness as ∆y a distance of y meter from the origin. So, the radius o...

Q: 1 3 4 f(x) f'(x) g(x) g'(x) 1 2 4 3 1 4 3 4 1 2 1 3 4 2 3) if h(x) = f(x) · g(x) f(x) 3) if h(x) g(x...

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Q: dy Find dx y = d'y %3D dx xp 2.

A: topic - derivative of a function

Q: (d) Use Stokes' theorem to evaluate S. F.dr where = z²î + y²j + xk and C is the triangle with vertic...

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Q: (a) Use partial differentiation to determine the expressions for in the following cases: (i) x³ + y°...

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Q: In this assignment you are required to answer for the following functions (c) For a differentiable f...

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Q: xニメー fx)=4x

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Q: (b) Sketch a condition to prove that the curl of a gradient is zero (0). Briefly explain your answer...

A: We need to prove curl of a gradient is zero. Note - As per our guidelines we can solve only one ques...

Q: Use the shell method to write and evaluate the definite integral that represents the volume of the s...

A: Given: y=x

Q: Find the Cartesian equation of the curve defined by the following parametric equations . after that...

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Q: (b) Sketch a condition to prove that the curl of a gradient is zero (0). Briefly explain your answer...

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Q: Let f(x) 4 cos x + 2 tan x f' (æ) = r(금)- f'

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Q: Find the first derivative of g(t) = ln| t7 g'(t) =

A: topic - derivative of a function

Q: lim - 25 Complete the table below. (Round your answers to four decimal places.) 4.9 4.99 4.999 5.001...

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Q: Compare the monthly cost of payments for $1000 loan at 5.5% for one year

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Q: Consider the position function   ​s(t)=−4.9t2+35t+16.   Complete the following table with the approp...

A: The solution for the above question is as shown below.

Q: A second-order differential equation is expressed by: y" – 3y' + 2y = e3t Solve this equation for y(...

A: Using method of Laplace transform.

Q: If f(x) = /x, find f'(13). f'(13) = (Type an exact answer.) %D

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Q: a) Evaluate f, (2x – z) dS, where S is part of the plane 3x + 2y + z = 1 that lies above the rectang...

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Q: (f o g)(1) =

A: Given query is to find the the value of composite function.

Q: Find the absolute maximum and minimum for the given pair. 4 5

A: To find out the absolute maximum and absolute minimum. 

Q: The table below gives the annual sales (in millions) of a product. 1998 1999 2000 2001 2002 2003 200...

A: Use avg rate of change formula

Q: Find the absolute maximum and absolute minimum of f(x) = +-35I over tl Time left 59:05:00 %3D Answer...

A: Solution is given below:

Q: Use the graph of g to find the value of each expression. If a limit does not exist, explain why. 4 4...

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Q: c) Find the volume of the solid bounded from the top by the surface f(x, y) = 2x +y² and from the bo...

A: Here is the solution of the given problem. Volume

Q: ind the area A of the region that is bounded between the curve f(x) = 4 sin and the curve g(x) = 4 s...

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Q: . 2x2 +2y? + 2z2 = 8x- 24z +1

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Q: 30С Compute the following limit of the Reimann sum by completing the steps. n(n+l) n² (n+1)? Use i=1...

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Q: (ry +y ) y' = y?. y' = エーリ+3 y' =

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Q: Q1 Determine whether the following differential equation are homogeneous, exact or inexact. Then obt...

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Q: To evaluate the indefinite integral x^2(x^3 + 1)^3/2 dx using method of substitution, answer the fol...

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Q: Differentiate the function. y = In(x) Need Help? Read It %3D

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Q: Evaluate the line integral ∫_c (2x − y) dx − (x+ 3y) dy , where C is a straight line from (1,1) to (...

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Q: Question For the function (1-z if z 1' evaluate the limit lim f(x). (If a limit does not exist, ente...

A: solution:-f(x)=1-x ,       if x≤1-x2+x ,   if x>1left hand side limit at x=1limx→1-f(x)=limx→1-1-...

Q: Consider the following. y = x2 y = 12 - x 16 14 12 101 8- 6- 8 10 12 (a) Find the area of the region...

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Q: y' - y = xe". a²y'+ay+2= 0.

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any ...

Q: Find the arc length of the graph of the function over the indicated interval. (Round your answer to ...

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Q: Differentiate the function. y = (3x-4) (2-x*)° dy %3D dx

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Q: Calculatey. xy+x°y=x+8y xy +4x-8 y' = x'y*(4x- 1) A -y-5xy y' = 4xy³+x4 1-y-2x 4xy*+x*-8 none of the...

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Q: -1, –1). Find Let A(-1, 3, 3), B(4, –1, 0), C'(5, 4, –7), and i. the normal vector to the plane ABC....

A: Note:- As per our company guidelines we are supposed to answer only first three sub-parts. Kindly re...

Q: 1. lim (3x + 2) X--3 2. lim(1-x2) -2x2+ 4) X-1 3. lim(3x

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Q: Question For the-function if a <-1 2x2-r-1 if a 2-1' -2- 1 f(x) = evaluate the limit lim f(x). Z-1 (...

A: Topic = Limits As per guidelines , At a time only one question can be answered. please repost fot ot...

Q: (a) Calculate and fully simplify |a° cos(x) dzr. Hint: Considering a mnemonic for integration by par...

A: Note- Multiple questions are asked, I am answering the first question. Please repost for other.

Q: 4. Find the polynomial function f(x) of degree 4 with zeros 2 (multiplicity 2) and 31, f(0) =36

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Q: Express the integrand as a sum of partial fractions and then evaluate the integral. dx 4 х —1

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Q: Calculate the integral, assuming that 6 f(x) dx = 2 and 6 g(x) dx = 15. (Give your answer as a whole...

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Q: Answer the questions about the following function. f(x) = 3x - x-2 (a) Is the point (2,8) on the gra...

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Q: 4. Sketch the graph of f(x) =Va+3 if r<1 and use it to make a conjecture for the values of %3D 2²-1 ...

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