1. Use mathematical induction to prove the given statements below. 2 3+2 32+....+ 2· 3n-1 = 3" – 3 for n > 1 a. %3D b. 1+4+4²+....+4"-1 = -(4ª – 1) for n > 1 3

Q: f fcx) = 5 Ccor"2x) 131

A: The objective of the question is determine the derivative of the given function.

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A: This question can be solved using the concept of methods of approximation of roots.

Q: 1. Find the derivative of the following: (Simplify your final answers.) f(x) = ev3(cos²zx) C.

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Q: (4) Evaluate S SR e™y-2dA where R is the region enclosed by y = 4x, y = }, y = ± and y = 1.

A: Let's find.

Q: Use the given information to find the indicated probability. An B = Ø, P(B) = 0.1, P(A U B) = 0.1.…

A: Solution - Given:-  P(A U B) = 0.1 ,  P(B) = 0.1  P(A) = ?

Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: The region is bounded by y=21-22, x-axis, y-axis and y=20 revolved about y-axis.

Q: uation of motion in the form x(t) = Ae™it sin( V2 – 2?t + w), which ft

A: answer is in next step

Q: 2. Which of the following is not an ordered field? Q=(all rationals) R=(all reals) S=(all…

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Q: 2. Use the Laplace transform to solve the initial value problem y" + 4y' + 5y = 2, y(0) = -2, y'(0)…

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Q: Let R be the quarter-circle region in Quadrant 1 bounded by the x-axis, the y-axis, and the circle…

A: See the answer below

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Q: Derivative of f(t) = 8^t[(2t+1)^2+t] using Chain Rule

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Q: (a³-8) g(a) = (Va²+4)* .3.

A: The given function,     ga=a3-86a2+43

Q: 24. Given z = 6x°y-e", calculate or z. A) 12y–x'e" B) 12y-ye" C) 12y-e" ху D) 12x - хуе"

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Q: sech j(r) = e

A: We know that derivatives of sechx is  d(sechx)/dx = -sechx.tanhx   Here i attached the solution of…

Q: 8. 21

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Q: Question 6 Use cylindrical shells to find the volume of the solid generated wher the region enclosed…

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Q: Answer the following using the chain rule (Complete solutions) 1. Differentiate f(x) 2.…

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Q: B a A b Note: Triangle may not be drawn to scale. Suppose c = 5 and A = 70 degrees. Find: a = b = В…

A: Solving the problem by finding the missing values of the triangle.

Q: Let y = f(x) be some function and suppose f(4) = 3. %3D If the tangent line to f at a 4 passes…

A: On solving this we will get

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Q: Consider the angle shown below with an initial ray pointing in the 3-o'clock direction that measures…

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Q: Find the function F that satisfies the following differential equations and initial conditions.…

A: F'''(x)=12xIntegrating both sides,⇒F''(x)=6x2+c1Integrating both…

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Q: f(x) = √x2−2​ ; x = 2 what is its derivative?

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Q: Question Approximate the local minimum value of the function given below. Use Newton's method with…

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Q: Find the volume of the solid that results when the shaded region is revolved about the indicated…

A: Given region is bounded by y=21-2x and y=20

Q: 1. Find an equation for the tangent line to the curve x= sin nt, y= t? - 3t at the point with t= 2…

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Q: evaluate the following integrals:

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Q: dæ is equivalent to Using the substitution u = x + 1 Vx + 1 1 -du 1/2 du du -1/2 du - 1) /u2

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Q: 200 D(r)

A: answer is in next step

Q: Evaluate the integral S SR 6x dy dx over the rectangular region R = {(x, y) |0 <x < 2, 0 <y < 1}…

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Q: The rectangles in the graph below illustrate a left endpoint Riemann sum for f(x) = on the interval…

A: We have to find the integral using left and right endpoints.

Q: (a³-8)° (Va2+4) g(a) = (Using logarithmic differentiation) 3

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Q: 1. Find the derivative of the following: (Simplify your final answers.) f. Q(x) = Jx + Vx + :+ ...

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Q: Find the consumer's and producer's surplus if for a product D(x) = 16 0.006z and S(r) = 0.003r2…

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Q: 1. Which of the following is 'alse? * If x > 0, then 1/x > 0. O If x > 1, then x*2 > x. O If x<y,…

A: Please see the answer below.

Q: 639 * The degree of the polynomial graphed above is Select an answer v Select an answer

A: Degree is the largest exponent of variable.

Q: 12)List the first five berms of Ehe regence a,=6, aan= 5a -4 as=3 a=? asz?

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Q: 5. f(x) = x(12.x + 8) 7. f(x) = 7x²/5+ 8x-4/5 %3D

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Q: Given the following acceleration function of an object moving along a line, find the position…

A: Given problem:- Given the following acceleration function of an object moving along a line, find the…

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Q: 5- If Die is rolled find the probability that never appear 2 a) b): d) 3

A: Answer is given

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A: Follow the procedure given below.

Q: A A A A A A A A A A A A A A A A A A A A A 2!, 22 23 16. The sum of the series 1+ 1! 2n 二十… is n!…

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Q: Suppose k is a non-zero real number. Evaluate the limit algebraically. If it does not exist, explain…

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