(t – 1,t < 0 g(t) 12, 0 < t < 2 2t, t > 2

Q: |(x² + a) 5 5x The resulting integral of dx is In +eTan-1X + C, where a, b, d, and e are integers.…

A: Given:        ∫5xx3+x2+4x+4dx Apply linearity:     =5∫xx3+x2+4x+4dx Factor the denominator:…

Q: What is the volume of the region R = ((x. y, z) e R'1 sxs 3:2 sy S 4:3 sz5 5)? %3D Select one: O…

A: Volume of the region R is given by volume=∫13∫24∫35dzdydx

Q: x'+8 if x + 2 The function f given by f(x) = is continuos at x = -2 x+2 -12 if x = 2

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Q: 4. If f(t) = 3 sin(4t + 0.12) – 2 cos(3t – 0.72) determine f'(t) when t 1 5. Evaluate when x 1,…

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Q: Solve the differential equation y tana+y = 3 sin r. %3D sin I A sin a B sin r + C Cos a c - sin I +…

A: We have to solve the differential equation: y'tanx+y=3sinx

Q: How can you relate antiderivatives as an opposite of derivatives in your life? explain

A: Solution is given below:

Q: x+V x+V X lim X- 00 V> V x+1 х+1

A: To evaluate: limx→∞x+x+xx+1

Q: Given the conic section 4x^2 - y^2 - 24x - 4y + 28 = 0 do the following:   1. Write the standard…

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Q: Sketch the region whose area is represented by the integral Só Suz dxdy.

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Q: 2) Find the equation of the tangent line to the curve y = cos(2x+ at x =

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Q: 00 Given: (1 + 2x)e*dx̟ Using integration by parts and letting dv 00 is %3D u = -1 - 2x, then the…

A: Let's find.

Q: B/Using the following table, find f(x) as polynomial in x: -1 0. 3 6. F(x) -6 39 822 Good Lup

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Q: True or False, If f' (3) = f" (3) = 0. then I 3 MUST be an inflection point. (Remember = to give…

A: It is given that, f'(3)=f''(3)=0 then x = 3 must be an inflection point.

Q: - CoS I 2. Find the indefinite integral / sin 2x e A 2e-sinz (sinI+1) + const B 2e-sin (sin I – 1) +…

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Q: ) Let R={(x.y): 0sx,Osy, +ys4) be enclosed region. The result of the following double integral (by…

A: Given region R=( x,y) : 0≤x, 0≤y , x2+y2≤4

Q: Compute the derivative of each function. f (x) = e³x* += (cscx + sec x)² %3D %3D

A: Follow the procedure given below.

Q: S csc6 cot* w dw W

A: Given,           ∫csc614wcot414wdw

Q: Evaluate the integral. (Remember to use absolute values where appropriate. Use C for the constant of…

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Q: discuss and sketch the graph of the given function f (x) = e" + x %3D

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Consider the Cardioid r = 2 − 2 sin θ. (a) Find its total arc length. (b) Determine the area of the…

A:

Q: 3(x + 2)\/1 (x+2)² Which of the following is *+2) + arcsin 9 +C equal to? arcsin (z + 2) + (x + 2)v5…

A: Given that,     92arcsinx+22+3x+21-x+2292+C

Q: 4. Suppose U = {1, 2, 3, 4, 5, 6, 7, 8, 9}, A = {3, 4, 5, 6, 7}, B = {all multiples of 3} and C =…

A: U=1,2,3,4,5,6,7,8,9A=3,4,5,6,7B=all multiples of 3C=all multiples of 2

Q: Compute the directional derivative and gradient of f(x, y, z) = 4r – yez at (2, -1,0) in the…

A: Given: fx,y,z=4x-y2e3xz       at     2,-1,0 Directional Derivative = Gradient of function x unit…

Q: (1 – x²)dx eTextbook and Media 2) V You answered correctly! Move on to the next part to add to…

A: According to guidelines we solve only first question.

Q: Find the derivative of the function y=(4x+1)^5(3x+1)^-4

A: We can find the derivative as below.

Q: 7) A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15…

A: Given: A spherical balloon is to deflated so that its radius decreases at a constant rate of 15…

Q: d太 2.

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Q: (9) If sin(A) = /2, sin(B) = - ½, "/½ < A < r, and n < B < 3*/2, find cos(A + B) (A) 0 (B) /2 (С) —…

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Q: Let E be the region in R that is under the plane x + 2y – z = 0, and in the xy- plane it is enclosed…

A: Find your answer below

Q: 5. Find two positive numbers whose sum is 10 and the sum of their squares is as small as possible.

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Q: 14. (x + 3x – 1) dx 15. dx tU +1) -G² – 1)]dy 16.

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Q: Evaluate the integral 3 2x cos(xy)dydx 2

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Q: 2. Jx2Vx3 – 27 dx -

A: As per rule of bartleby we can solve only one question at a time and we can solve only three subpart…

Q: Using Trigonometric Substitution  ∫ dx/ (x^2+x+1)^(3/2) find f theta

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Q: 4. The surface described by the equation x2 + y + z² = 0 is a(an) (a) elliptic paraboloid symmetric…

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Q: 4. A father is running west at 5 m/hr and his son is running north at 6 m/hr. Both are headed for…

A: I am attaching image so that you understand each and every step.

Q: cos x Given: tan x dx. Using trigonometric transformation , the integral in terms of u is sin x Cos4…

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Q: Evaluate | 4x2 + 4x + 5 dx

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Q: Decide on what substitution to use, and then evaluate the given integral using a substitution. (Use…

A: Use the algebraic substitution and solve the integration.

Q: Question- Let R be the region bounded by y= x+2, y30, and x=3. Then draw the region and evaluate the…

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Q: Find the magnitude of the vector a and the smallest positive angle 0 from the positive x-axis to the…

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Q: Given: dx Using trigonometric substitution, solve for the integral form in terms of 0. 0 d® B sin² 0…

A: Given: ∫x2-9x3dx Let I=∫x2-9x3dx   To solve this integral we need to do the trigonometric…

Q: x² – 9 dx ? Using trigonometric substitution, what is A) none of the choices 1 seç x² - 9 + C (В +…

A: Sec²(t)-tan²(t)=1 Sin²(t)+cos²(t)=1 Sin(2t)= 2sin(t)cos(t) 2sin²(t)= 1-cos(2t)

Q: give the equivalent cartesian coordinates of ρ = π

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: 1. Prove the following limit. a) f(x)=x²+2x+6 where lim, 3 f (x)=21 x→3 b) limx? -x+1=-5 c) lim x→2…

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Q: 4) For each graph in Figure 16, determine whether f' (1) is larger or smaller than the slope of the…

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Q: 3x² +7x+28 f(x) x2 + x+7 A Using partial fraction, evaluate x3 + x2 +7x aX the decomposed fraction…

A: The objective of the question is evaluate the indefinite integral in partial fraction.

Q: sec(0) Compute the area A bounded by the line r = 7 e and the rays 0 = 0, and 0 = 4 as an integral…

A: Here, the formula used is: A=12∫abr2dθ

Q: A 10-foot ladder is standing vertically against the side of a building. To show you a related rates…

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Q: If f(x) =x* -+5VxG + 7 find f(-4) 1.

A: