Find the values of a and b that make f continuous everywhere.

Q: Write a definite integral that represents the area of the region. (Do not evaluate the integral.) Y1…

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Q: S- x³dx is equivalent Vx²-4 Using trigonometric substitution,

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Q: Find the general solution of the following: 1. (4D2 – 4D + 1)y = 0 %3|

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Q: 7) Last problem!!! I want you to compute both sides of the equation in the Divergence Theorem The…

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Q: A box with a square base and open top must have a volume of 415292 cm. We wish to find the…

A: topic - application of derivatives

Q: 4y" – 4y' + y = e"/2/1 – x².

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Q: Evaluate the double integral. 7x sin y'dA; Ris the region that is bounded by y = x², y = -x', and y…

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Q: Find V· (V × F) if F(x, y, z) = 7 sin xi + 5 cos(7:x – 8y)j + 6zk. V . (V × F) :

A: F(x,y,z)=7sinx i+ 5 cos( 7x-8y)j+6zk

Q: 1. Find the equation of the normal line at a given point. y = - @ (5,1)

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Q: Evaluate the integral / (12x + 18y)dx + (12x – y)dy along the paraboli - arc y = x² from (0,0) to…

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Q: 3x. If sales are increasing ompany's revenue from selling a units of an item is given as R = he rate…

A: Given query is to find rate of change of revenue.

Q: Evaluate: /x*V1-x*dx A None 3 글(1-x4) 2 +C В 3 -(1-*) C 3 (D (1-x+) +c - C 3 은(1-x) 2+C

A: We have to solve above question and find integral

Q: b. S 2*³-4x²-x-3 dx х2-2х-3

A: First we divide the polynomial  using long division

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Q: Ty csc?y dy is equal to A —у сoty — coty dy - Scon dy у сoty coty dy с) -у соfу+ coty dy D) None E у…

A: Integrate by parts.

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

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Q: Determine the equation of the tangent plane and normal line to the surface at the given point.…

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Q: cosxsin?xdx Solve using algebraic substitutionf V1+sinx

A: We have to find Integration using algebraic substitution.

Q: Use the given vectors to find v•w and v.v. v = 61 - 4), w= - 21 -J v•w= 2 (Simplify your answer.)…

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Q: Find the area of the plane region bounded by y = x2 - 4x and y = x(2 - x)

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Q: 2. Evaluate f'(5) for y = v2x² – 1 hor Ju OIT

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Q: L (7+ 4)(x + 3)dæ = 74/3 %3D Select one: O True O False

A: The given integral,       ∫-11x+4x+3dx=743

Q: 2. Evaluate f'(5) for y = v2x² – 1

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Q: Which integral corresponds to the area of the shaded region between the curves y = -x? + 3x and y =…

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Q: | (csc 0)(1+ sin? 0 + sin 0 cot? 0) do а.

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Q: Find the derivative of y=x^(7sinx). (x>0).

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Q: Find T(t) and N(t) at the given point. r(t) = 8 cos(t)i + 8 sin(t)j; t= 3 T() N(G) .3

A: To find the vectors T(t) and N(t)  for the given r(t) at point t=pi/3.

Q: ||r'(t) × r"(t)|| Use the formula k(t) to find k(t). %3D 13 r(t) = e12'i + e'j 156 el4t K(t) : (V144…

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Q: For the given vectors a and b, find the cross product a x b. = (4, 0, –3), b = (2, 3, 0) a x b =

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Q: S- x*dx is equivalent to Using trigonometric substitution, (A) 6 sec40 de B) None (c) 8 sec40 de D 8…

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Q: ired) and other rules; You can use technology

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Q: x+1 1.

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Q: Find the equation of the line tangent to the function f(x) = (x – 1)3 + 2 at x = 1. O y = 2 O y – 2…

A: Given query is to find the equation of the tangent at x = 1.

Q: y = zsin z

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: Find the value of n in the following definite integral. S“ 4x*dx = 1

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Q: 5. Evaluate the indefinite integral sin2x 1+ cos?x

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Q: 1. The number of arbitrary constants in a particular solution of a fourth order differential…

A: 1. We know that the number of constants in the general solution of a differential equation of order…

Q: Find the area bounded by the indicated curves. y = x4 - 18x? + 81, y = 81 - x

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Q: Solve the logarithmic equation algebraically. Approximate the result to three decimal places. (If…

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Q: Describe the graph of the equation. r = 7 sin 6t i – 7 cos 6t j O It is a circle of radius 6 in the…

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Q: So 32 (z + 4)° da = 5120 %3D Select one: O True O False S sin4a da = 4 7/3 7/12 %3D Select one: O…

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Q: Since log,(a) = c → a = b°, 1--2 In(즉)- e-1/2. » X = So, y' = 4x(1 + 2 In = 0 when x = -1/2 and y" =…

A: Since logba=c→a=bc                          1=-2lnx5  ⇒-12=lnx5  ⇒e-12=x5⇒5e-12=x⇒        x=5e-12

Q: Suppose that f(x) is a differentiable function satisfying the data in the table below on the…

A: Left -hand approximationa=4 , b=12  ,n=4∆x=b-an∆x=12-44=84=2Subintervals are 4,6,6,8 , 8,10 ,…

Q: 2. Vector v has a magnitude of v53 and a directional angle of 164.055°. Select the response below th…

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Q: The particular solution that satisfies the differential equation and the initial condition dy/dx =…

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Q: Solve the given differential equation by separation of variables. csc(y) dx + sec2(x) dy = 0

A: This question is related to differential equations, we will solve it using given using given…

Q: 7. Sketch the region of integration, and evaluate the integral. 2 2x. JI zdz de dr .2

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Q: Find the exact area under the curve between the indicated values of x. 3 ; between x = 1 and x = 3

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