f(t) = t−3 Find  f '(t). f '(t) =          Find the slope of the graph of the function  f(t)  at the point    1 2, 8

Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

A: Given problem:- Find the volume V of the solid obtained by rotating the region bounded by the given ...

Q: Given the differential equation y" - 4y' = 0

A: given differential equation is -  y"-4y' =0   

Q: Another - the following. a) Set up an integral for the volume a solid torus (the donut-shaped solid ...

A: (a) To set: The integral for the volume of a solid torus. Given information: radii br and aR, a=7, b...

Q: What is lim ? X-0+ x

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Q: Evaluate. 3 If f(2)dz = and 9(=)dz = - 1 what is the value of g(x)dx [6f(x) + 29(z)]dz =?

A: Topic = Integration

Q: y Sales of Version 4.0 of a computer software package start out high and decrease exponentially. At ...

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Q: Evaluate: * (Зх— 1 f(x) = {5 (x + 2 x 2 x = 2

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Q: 2m-1 Σ m=1 (2) (m!) (m+x+1) How did he get the value inside the circle, can you explain step by step...

A: Jv(x) = ∑m=0∞ -1m . x2m+v22m+v .m! (m+v)!

Q: Evaluate: (x² – 1 х1

A: Topic:- limits and continuity

Q: The integral of any quotient whose numerator is the differential of the denominator is the LOGARITHM...

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Q: Let f be continuous and have an inverse. Write F as the antiderivative of f, i.e., F(x) S ƒ (x)dx. U...

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Q: x + 2x – dx

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Q: Detemine the x-values at whìch, 9水)= 2xー 3xー+X メt,xE - スxナラメー3x underined. Evaluate the linit ac xap...

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Q: (a) D = (x + z)a, (b) E = (y² – x³)a, + xyza, + (x² – z?)a.

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Q: is continuous at x=3, f (-1) =6 ? + a, x # 3 3b, x 3 ontinuous at x=2? - x > 0

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Q: Determine the value of x of the continuous function: * (x – 1 x 3 f(x) = {3x – 3 Зх — (-4x + 3

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Q: . Ssec(x),/sec(x) + tan(x)dx

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Q: dy - y = xy2 dx

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Q: 1. Use Lagrange multipliers to find the maximum and minimum values of f(x, y) = 4x - y subject to th...

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Q: Given the differential equation, its particular solution, and its wronskian –7x y" + 2y' - 35y = 4 e...

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Q: x+1-cos²(x) 3sin(x) 7. Find lim

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Q: Question Select your answer. For what values of x is f(x) = 2 tan x + + nn, n E Z 3 discontinuous? ,...

A: Find your answer below 

Q: Given that f(x) = 5x° + x³ + 2, find the derivative of f- by using dy che formula d.x 1 Check dx you...

A: To find: The derivative of inverse of f(x)=5x5+x3+2 by the formula dydx=1dxdy. Calculation: Find the...

Q: 1 4lnr Evaluate: | (A +C - 2(r5 – 3) +C 2(,5 – 3) 2 +C 15 4lnr 4

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Q: 3x (2) Determine the inverse of the function ƒ(x)= 2x -5

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Q: If an object moves along the y-axis (marked in feet) so that its position at time x (in seconds) is ...

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Q: sinrdr In( ou In cosr -3 cosr -3

A: Indefinite integral

Q: 2. (a) Determine whether the Mean Value functions on the given interval [a,b].

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Q: 5. Does the function f (x) = -2x³ + 2x2 + x- 1 ever have a negative slope? If so, where? Explain and...

A: Topic:- function and it's properties and derivatives

Q: Evaluate: / 3'/ | 3° +4dy A 3' +4) : In27 +C A 2 (3+4) +C B.

A: Integration

Q: |(9 cos(9 x) +4 sin(4 x))dx =sin(9 x) - os Select one: True O False

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Q: 'd = eAt kdt A True B B False

A: I am going to solve the given problem by using some simple calculus to get the required result of th...

Q: 3. Evaluate

A: The given integral is 1/(x-1)2/3 limit from 0 to 3.

Q: F. Find the moving trihedral of the curve C of F(t) = at t = ; 2'

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Q: In (sin2x) sin2xdx Evaluate; sin³x -+C 3 A sin?x +C 2 B В sin4x - +C 4 sin4x D -+C E None

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Q: Choose all sets that are countable: O (-0.5, 11.5] n Z O (-0.5, 7.5) O NU{-1} O {3k|k € Z} 1 n e N n...

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Q: A 3" + 4) 2 +C In27

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Q: Give the degree and leading coefficient of the following function: f(x) =2x2 (4- 3x-5x3)

A: Given query is to find the degree and the leading coefficient of the function.

Q: (х +у—4)dx — (х — у + 2)dy %3D0 -

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Q: The vectors u = (-7, 1, -2) and v = (-28, x, - 8) are parallel if and only if x = - 212 %3D Select o...

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Q: Given the differential equation y" + 7y' + 12y = 8x e-3x Determine the General Particular Solution f...

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Q: Determine the limit of the following: 1.1) lim x -->3 (sqrt 3x / x sqrt x + 1) 1.2) lim --> pi / 3...

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Q: Which of the following series converges and which diverges? Find the sum of the convergent series. 0...

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Q: A spherical balloon is inflated with air flowing at a rate of 15 cm/s. How fast is the radius of the...

A: The formula to calculate the Volume of the balloon is:              V=43πr3 where r is the radius of...

Q: 1. Determine whether the series converges using any appropriate test. Identify the test for converge...

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Q: Use Newton's method and find an approximation for the root of the following function accurate to wit...

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Q: Determine if the given function is continuous at 3. * x² + 3 f(x) = {3 – 4x (x – 12 x< 0 0< x< 3 %3D...

A: Given the query is find function is continuous or not at x = 3.

Q: Section 3.5 p. 315/317 # 288 Use tables to perform the integration. dx 288 V4x+1

A: We have to find the integral.

Q: Find the arc length of the curve r(t) = (2t3/2, cos 2t, sin 2t) from t = 0 to t = 1. %3D

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Q: Find the volume V of the solid obtained by rotating the region bounded by the given curves about the...

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