Instructions: Use Rules of Differentiation to differentiate the following functions. Show your solution and simplify your final answer. 1. y = 9x2/3 + 4. h(x) = (3x + 4)² sin x-1 2. g(x) = cos x

Q: csc S- |cot2즐x)-4cot(를x) +4 Given: Find: u cot -2 O ca) cot 4cot x+4 cot +4

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Q: Use the shell method to set up a definite integral (set up only, do not evaluate the integral) for t...

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Q: 8. dx du The integral reduces to k, where u = f(x) and for some ex + 1 constant k . Compute f(1). e ...

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Q: 2 cos(За? + 5) + [62? + 2] (а) lim За2 + 5 0)2

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Q: III. For each of the following functions, find the indicated derivative using the definition. Show s...

A: As per our guideline if multiple questions are posted we are supposed to answer only the first one. ...

Q: sec3(In x) + sec²(In x) tan(In x) dx Given: 2x Find: du V sec (In x) + sec²(In x) dx tan(ın x) dx ta...

A: On solving this we will get

Q: Use sigma notation to write the Maclaurin's series for the function f(x) = x cosx Show complete solu...

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Q: Graph the function f(x)=−4x2f(x)=-4x2 and draw the tangent lines to the graph at points whose x-coor...

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Q: dx reduces to du The integral 3. ex + 1 where u = f(x) and for some и constant k . Compute f(1). (a)...

A: Given

Q: = 60 %3D = 30 %D =D3 %3D = ? %3D

A: From the given information,           3 × times of Red flower = 60                        

Q: 1+ In x 6. Find f(x) so that when u = f(x) the integral J tan(f(x)) dx can be rewritten as | cot u (...

A: Solve by integration

Q: e) Explain how one can use differentiation to analytically determine the slope of a curve

A: If cost revenue given , we differentiate it so we give marginal revenue. 

Q: The average student enrolled in the 20-week Court Reporting I course at the American Institute of Co...

A: Given query is to find the function N(t).

Q: -8 Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval....

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Q: 14. Find dr/de: r= 0 sin 0 + cos 0 а. cos @ b. 0 cos 0 0 sin 0 C. O a O b

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Q: e2t+a (2 cos at – 3 cosh 2at) -

A: We have to find Laplace transformation. 

Q: Find dydx for y=ln2x3−x2

A: This question is based on derivative.

Q: (b) Let u = u(x, y) and f and g be twice differentiable functions. Then, a general solution to the e...

A: The objective is to find the general solution u(x, y) .

Q: Find an equation of the tangent line to the graph at the given point. (The graph is called a Witch o...

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Q: dx x Vx²+2x-1

A: Evaluate the integral∫1xx2+2x-1dx

Q: c) TR = (/Q5).(InQ)

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Q: Evaluate /| F - d5 , where F = and S is the helicoid with vector equation r(u, v) 0 < u < 4, 0 < v...

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Q: 5. Solve a) In(x+1) = 3 b) e2 – e = 2.

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Q: Calculate the respective marginal functions for the following total cost/revenue functions. you stat...

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

Q: 15-16 Find the number e that satisfies the conclusion of the Mean Value Theorem on the given interva...

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Q: Describe the sampling distribution of p. Assume the size of the population is 25,000. n= 600, p = 0....

A: Here given that, Population(N)=25000 n=600,p=0.1 Now, n≤0.05N600≤0.05*25000600≤1250 ............(1) ...

Q: 23. If u = f(x), then +2x² + 1 k + C for some constant k . x² + 1 Compute kf (1). (a) ¼ (b) – ½ (c) ...

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Q: Find the nth Taylor polynomial for the function, centered at c. f(x) In(x), n = 4, c = 3 PĄ(x)

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

A: Our Aim is to determine the Laplace Transform of the functions shown below:-14cosh (16t)+16sinh (16t...

Q: -2 3. Integrate: [8x°e"-2 dx = du - e* 4x°dx 2 du = dex?. 4x° dx 4 3 2ou 8 ex".x°dx

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Q: cSc x du 5. If u = f(x), then -. Compute f dx = sin x – cos x 2 (a) 1 (b) -1 (c) 0 (d) 2

A: ∫cscxsinx-cosxdx=∫duu

Q: Use the Alternating Series Test to show that the series is convergent. +oo (-1)"+1 Σ 3n n=1 Answer i...

A: The objective is to use alternating series test to show the convergence of the given series.

Q: dx 2х — 10 15. Evaluate A. Ο В. 1/2 С. C. 00 D. - 00

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Q: sec (In x) + sec2(In x) tan(In x) 2х Given: dx Find: du tan(in x) 2х sec³(In x) + sec²(In x) sec(in ...

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Q: 18. dx The integral - can be rewritten as V1 - x (a) lim (-2+ 2v1-s) (b) lim (-1+2vī -s) s--00 s--00...

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Q: 2 tan(4x-1)–3 cos²(4x-1) dy cos(4x-1) 4. If we let u = 4x -1 for the ', what's going to be the resul...

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Q: Find the equation of the line through P = (8, 7) such that the triangle bounded by this line and the...

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Q: Use Stokes' Theorem to calculate the integral | F. dr where F = (y – x)i+ (z – y)3+ (x – 2)k and C i...

A: Solving the following integral problem

Q: Solve the following differential equations. Indicate the (Differential Equations) method/s used at t...

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Q: arctan(xy) = arcsin(3x + 3y),    (0, 0)   find an equation of the tangent line to the graph of the e...

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Q: csc2 Given: lcot2(클x)- 4cot(글x)+ 4 xp - Find: u cot2 4cot x+ 4 cot cot2 4cot X+4 O ca)-2 cot

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Q: Find the laylar polynomials of orders = 0,1,2,3, and 4 about x = No, and then find the nth laylor po...

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Q: y(x² – y² + 1)dx – x(x²-y² – 1)dy = 0

A: Exact differential equation

Q: SV + 2) /2 – 3y dy -

A: The detailed solution is given below Thank you 

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

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Q: Some scientists believe that the average temperature of the world has been rising steadily. The aver...

A: We have to find slope and T - imtercept And T (surface temperature in 2050) 

Q: Illustrate the Quadratic Funictions Using table of Values Think About This! Consider the table of Va...

A: Quadratic

Q: dx Evaluate 6e* cos (3e *) O 2 [In |sec(3e-x) + tan(3e-|] + C In |sec(3e-M) - tan(3e-|] + C O -18 [I...

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Q: 2. In each of the following, find fyzz, fryx, fxyz. 2. f(x, y, z) = lIn(xyz) + 2² tan¬'(e"Y)

A: I am attaching image so that you understand each and every step. Note:-  2nd subpart is more complex...

Q: Sketch the curve of y= 3x-10x³-12x²-7

A: The objective is to sketch the graph.