Find an antiderivative of the function. (a) h(q) = sin(q) H(g) = (b) f(x) = 3eX F(x) =

Q: Ssin(x)cos(2x)sin(3x) dx sin(3x)cos(3x), sin(2x)cos(2x) , sin(2x) + + C 12 8 8. 4 sin(6x) sin(2 x),…

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Q: Evaluate the integral [cot5 x csc x dx O 1 1 늑csc? x-cscs x + 하sc3x + C 2 X + x + C 2 esc x + 1 csc?…

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Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

A: Given function F(x,y)=( 2x-6y ) i+(-6x+14y-7) j

Q: 3. Prove: a) Bo(U,4,)=U,(BO4) b) BU(N,4)=N,(BU4)

A: a) B∩∪iAi=∪iB∩Aib) B∪∩iAi=∩iB∪Ai

Q: Answer the following True or False. Letting u 4 1' produces: .2 2.x d.x. z2 1 du. 4. True False

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Q: Find the two x-intercepts of the function f and show that f'(x) =0 at some point between the two…

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Q: The graph of f is shown. Apply Rolle's Theorem and find all values of c such that f(c) = 0 at some…

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Q: Find the first partial derivatives of the function. f(x, у) = 3x + 5y + 4 fy fy

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Q: 3) y = 2 - 3y; y'

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Q: 2x-1 11. y = 5x+2 12. y=(5x² + 2x + 1 )3 13. y = V2x + 6 /14. y = 15. x = 2x + 3, what is dy/dx? =…

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Q: The equation r(t) = (t + 3) i + (7t) j+ (3t) k is the position of a particle in space at time t.…

A: Let's find.

Q: tan (x) J Cos cos“(x) 하an7(x) + 늑tan®(w) +C O tan'(x)7tan?(x) +9]+ C tan7(x) 36 O sin…

A: Here we have to integrate the given function.

Q: 15х2—х3— 43х — 19 Ax + B C The integral /- D + rx +s -dx can be rewritten as dx. (x+1)2(x²– 6x + 13)…

A: The integral ∫15x2-x3-43x-19x+12x2-6x+13 dx can be written as ∫Ax+Bax2+bx+c+Cmx+nt+Drx+s dx.To…

Q: sec(3r2 + In 2) evz+2 +9 a. y =

A: Use simple differentiation formula.

Q: .3 The result of dx is F(b) – F(a), where F(a) and F(b) are real numbers. What is the value of F…

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Q: 2x4 + 3x2 – 1 Rewrite dx as integral of sum of partial fractions. (x³ – 4x² + 5x)? C(2x- 4) +D E(2x…

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Q: Let f(x) = V53 - a The slope of the tangent line to the graph of f(x) at the point (4, 7) is The…

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Q: 1. Evaluate the following limits. 2 - V2a + 10 a. lim 2-3 22 +r - 6 4x – 7 lim с. -1- (3r2 – 2.r 5…

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Q: dx 4 sin e+C express the answer in terms of x. 3 Using Trigonometric Substitution (x² + x + 1) 2 4/3…

A: Given problem:-

Q: 2х — 1 dx x² – 6x + 18

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Q: Three pens of the same size are to be built along an existing fence. If 480 feet of fencing is…

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Q: 4. Find dy/dx og y = xsinx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: У(2 — 2х)100 — у — хz; ху and yz.

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Q: Vx2 + 4x - 5 dx = Using Trigonometric Substitution f(e)dA find the new limits of integration. 1. x+2…

A: Let's find.

Q: Solve the equation. Write the solution set with the exact solutions. log, (3-m) + log, (-m-2) =2 If…

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Q: 2x4 + 3x² – 1 (x² – 4x² +5x)? B(2x- 4) + C Rewrite dx as integral of sum of partial fraction D(2x-…

A: Here we have to apply partial fraction.

Q: Evaluate the integral Scot? x dx -cot x - x + C cot x + x + C cot x - x + C 1 cot x + C .3 X + O O

A: Topic = Integration

Q: Difference of quotient for 1/(x+4)^2

A: The given function,       1x+42

Q: (2x + 4) + 1 (2x +4) +1 dx: x2 + 4x + 5 x2 + 2x- 10 2 2 2 Consider dx = x2 (x2 + 4x + 5) dx evaluate…

A: We can solve as follows

Q: 2x3 – x² + x + 2 -dx = A + dx find A+B+ C+D- X+1 Consider x4 + x3 2 O 5 O 4 3

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Q: Solve the equation. Write the solution set with the exact solutions. Inx+ In (x-4) In (3x-10) %3D If…

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Q: | x(5*)dx x(5*) In 5 + C (In 5)? x(5") In 5 5* + C (In 5)² O A x(5*) In 5 + C In 25 x(5*) In 5 + C…

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Q: y" + 4y' = cos(t – 3) + 4t, y(3) = 0, y'(3) = 7

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Q: [2x+11 3 1 dx . evaluate Consider 3 1 dx x+3 dx = x2 + x- 6 x- 2 | x+3 X- 2 x+3 x- 2 In +C x+3 In…

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Q: f(x) – f(7) g lim x-7 x - 7 se symbolic notation and fractions where neede

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Q: 1 2. (33.6) Use the building block > a", |r| < 1, to find a power series representation 1–x n=0 for…

A: Solve the following

Q: 9х2— 6 To evaluate dx using the method of partial fractions, the given integral can be rewritten as…

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Q: A bacteria culture grows with constant relative growth rate. The bacteria count was 2,560 after 4…

A: answer in next step

Q: .4 x²+4x-5 Consider dx using Trigonometric Substitution find X- 1. x+2 -2 +3 sec 0 3 sec e -2 + sec…

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Q: Evaluate S. F dr where F(x, y, z) = e'i+ (xe + e²) j+ye²k and C is the line segment from (0, 2, 0)…

A: answer is in next step

Q: Evaluate the surface integral. xz ds, S is the part of the plane 2x + 2y + z = 4 that lies in the…

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Q: Sx³ Vx? +4 Svdu- Using Integration By Parts, dx = uv-

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Q: dx 4 -sin e+C Using Trigonometric Substitution - = , express the answer in terms of x. (x² + x + 1)…

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Q: Use the definition of a Taylor series to find the first four nonzero terms of the series for f(x)…

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Q: | cot2 x dx 1 ot x + C cot x - х + с cot x + x + с О -cot x —x+C

A: Given query is to find the the integral.

Q: 2x3- x² + x + 2 dx = D dx find A+B+ C+D. + x+1 + Consider x4 + x3 4 O 3 O 2 O 5

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Q: A    26    foot    ladder    is    sliding    down    a    vertical    wall.        The    base…

A: Consider a function y= f(x)  then the derivative f '( x) is the  rate of change of y with respect to…

Q: Rewrite the expansions in terms of exponential and simplify the results as much as you can. cosh 5x…

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Q: 2x4 +3x2 - 1 Rewrite -dx as integral of sum of partial fractions. (x3 – 4x2 + 5x)?

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Q: S2x². uv- Svau Using Integration By Parts, dx = uv- uv- Jva Find du

A: Our Aim is to solve the integral given below using integration by parts∫2x2e13x -(i)