-2r 2. Find de/dr of the function 0 = (cos(r))

Q: Using diliferentials, determine the appropriate O a. 47.1 cm3 Ob.314.2 cm3 OC 15.7 cm3 O d. 539.5 cm

A: Given query is to find the the change in the volume of sphere.

Q: (2.13) Compute Lp(t), where P is the regular tetrahedron with vertices (0,0,0), (1,1,0), (1,0,1), (0...

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Q: A thick spherical shell occupies the region between two spheres of radii a and 2a, both centred on t...

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Q: Determine the degree of each of the following polynomial functions. a. f(x) = 1+ x + x² + x³ Degree ...

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Q: x 2 f(x) = -

A: Using continuity of polynomials function,

Q: y y = 2 2 1 y = 1 → X п/2

A: The given question has been solved in detail. 

Q: Problem 2: A piece of string whose length is given below is cut into two pieces. One piece is used t...

A: The length of string is 48 cm.Let the length of the one piece is x,Suppose, equilateral triangle wit...

Q: dx 2V x3 - 3x x

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Q: sin 6z Evaluate: lim エ→0 00 O1 Which among the following limit theorems were applied? sin x O im エ→0...

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Q: X- S- V3e2x - 2e-2x dx VZe-2x+ /2e-4x - 3 +C 2/2 2/3e2x - 2e-2x + C V2e-2x +C 1 -Arcsin 2 V3 -Arcsin...

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Q: sec (In x) + sec2(In x) tan(In x) dx Given: 2x Find: du

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Q: () dix + (") dy = 0 (x3 x³+y3• (**) dy = 0

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Q: The graph of a function f is shown below. 2 -4 4 -2 -4 For the following questions, note that you ca...

A: ?As per our company guidelines we are supposed to answer ?️only first 3 sub-parts. Kindly repost oth...

Q: If $1500 is invested at an interest rate of 3.5% per year, compounded continuously, find the value o...

A: topic - exponential function

Q: Which of the following graphs show a removable discontinuity. (Select all that apply)

A: For removable discontinuity,   limx→af(x)  exists but f(a) not defined. For non removable discontuit...

Q: Consider the function f(r, y, z) = ry+y? + 22. (a) What is the gradient grad f of f, and what is its...

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Q: dx Evaluate 6ex cos (3e X) O 2 [In |sec(3e-x) + tan(3e-)|] +C [In |sec(3e-) – tan(3e-|] + C 1 In |se...

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Q: dx Given: Vx sin/x Find: Formula o Sesc u du O2 fcsc u CSC du O 2 sin u du Ssin u du

A: Explained below 

Q: Apply derivatives to determine the critical points of the function ?=?(x−6)².

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Q: Write an equation for a rational function with the given characteristics. 4, x-intercepts at (-4,0) ...

A: Explained below 

Q: Identify all three (distinct) solutions to the equation z3 = 27i. Write your answer in x + iy form.

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Q: e2t+a (2 cos at – 3 cosh 2at) -

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Q: Csc- X S- /cor?(x)- acot(=x) + 4 Given: dx cot(슬x)+.

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Q: dx Given: 2x- 3xlnx Find: du dx dx 3 X

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Q: z° – 6z' + 4z – 2 dz |

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Q: Evaluate 1 + x2 + y?dS, where S is the helicoid with vector equation r(u, v): 0 < u < 2, 0 < v < T

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Q: dx x² Vx²-1 -2.

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Q: 16. Explain the squeeze theorem using any example of your choosing.

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Q: Question 2: Illustrated below are two tangent lines drawn at 2 different points on the curve whose f...

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Q: f(x) = { * ах 2 + ах —4, х> 2

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Q: Determine the Laplace Transform of the functions shown and simplify.

A: We can evaluate the Laplace transform of the given function by using the following formula.

Q: Find the equation of the tangent line to the graph of the given function at the given value of x.   ...

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Q: Calculate the iterated integral. 36(u – v)³ du dv

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Q: 17. Let f(x) - (x- 3)Show that there is no value ofc in (1,4) such that /(4) not contradiet the Mean...

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Q: Calculate the Taylor polynomials T2(x) and T3(x) centered at æ = 8 for f(x) = In(x + 1). T2(x) = In ...

A: Please see the below picture for detailed solution. 

Q: 1 dx 1+Vx

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Q: 3. The area of the region under the curve y = 6z bounded by the lines z = 3 and z = 5 above the I-ax...

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Q: Graph the function f(x)= -3(x)^x +7

A: The given function is  f(x)=-3(x)x+7

Q: MAT

A: Graphical representation:

Q: f(x) = (x2 + x) (x* - 6x)3 %3D

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Q: Consider the following rational function: anx" + an – 1xn-1+ ... + a1x + ao f(x) bmxm + bm - 1xm-1+....

A: The rational function,      fx=anxn+an-1xn-1+....+a1x+a0bmxm+bm-1xm-1+....+b1x+b0

Q: 4 4e | f(z) = as x approaches 0 using the table of values? !! I. II. -1 -0.5 -2 -0.1 -1.5 -0.01 -1.1...

A: To find the limit at x tends to zero. We need to find limit near to the value x=0 There are four opt...

Q: Use sigma notation to write the Taylor series about x = function. 1 x + 5

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Q: 3. y³x2 – cos- sin x² + esin x = 1 y DIFFERENTIATE THE GIVEN

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Q: 4-x lim x-4 Vx-2

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Q: Discuss the continuity of the function g(x) = 1/(x^2-4) on the interval (0, 2] and [−1, 3].

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Q: Find all solutions to the following first-order differential equation.  Make sure the solution set d...

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Q: The area of a circular sunspot is growing at a rate of 500 km/sec. (a) How fast is the radius growin...

A: Note that, the area of a circular sunspot is A=πr2 So,  dAdt=π2rdrdt⇒dAdt=2πrdrdt...(1) Now, given t...

Q: a. Suppose the function f is updated from f(x) = x* to f(x) = – 4 · a*. How does changing the coeffi...

A: Multiple questions are asked, I am answering the first question.

Q: Find an equation of the tangent line to the graph of the function at a given point. Note: You may/ma...

A: Equation of tangent at point a,b with slope ,dydx.y-b=dydxx-a1. y=6x2+1    ; 1,3dydx=6×-1x2+12×2x=-1...