10.) Express the integral f sin 100 xcos 301 xdx in the form fp(u)du where p(u) is a polynomial and also state what the function u should equal in terms of x. You do not need to evaluate the integral in u and work out the final answer. For example, if the integral had been f sin7 xcos xdx, the answer I would want is that fsin'xcos³xdx = f-u³(1-u²)³ du and u = cosx.

Q: 2. Use the Intermediate Value Theorem to show that the equation has at least 2 positive real roots.…

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Q: Differentiate the following functions using the quotient rule. a) You are given that f (x) a df dx…

A: The Power Rule:The Chain Rule:The Quotient Rule:

Q: What is the coefficient of the x term in Maclaurin polynomial for sin(2x)

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Q: Use the product rule to differentiate the function h, where a and b are real numbers. h(x) = e¯ax…

A: According to product rule, if f(x)=u(x)*v*x) then f’(x)=u(x)*v’(x)+v(x)*u(x).

Q: How do you know that the functions sin x, ln x, and ex are not polynomials? Give reasons for your…

A: Polynomials have finite terms. And it has a highest degree.  But sinx , lnx and ex have infinite…

Q: 2. If f(g(x)) = sin x + 3sinx - 1, determine possible expressions for f(x) and g(x), where g(x) # x.

A: (1st method/way): Let f(x)=x²+3x-1 and g(x)=sinx Then we can find f(g(x)) as follows…

Q: Find the finite difference formula for the second derivative at point x=x; with points X₁, Xi+1,…

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Q: 5. Evaluate: 34 l vo dx dx. √9-16x2 0

A: To find the value of given integral.

Q: Calculate the number of real roots for f(x) = 13x' + 2x² + 8x using Rolle's Theorem. (Give your…

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Q: 1. Find the fourth Maclaurin polynomial for f (x)= sin 2x.

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Q: The best suitable method for approximating a zero of the function f(x)=sin x +cos x - x -1 is:…

A: Plot graph of the function:

Q: 1. Differentiate the following functions a. f(x) = sin(x) cos(x)

A: According to bartleby guidelines we supposed to do the first one of multiple questions kindly repost…

Q: Show that the function f(x)= x^3 − 15 cos(pi x) + 1 has three zeros in the interval [−4, 4]. Do not…

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Q: Assume that the number of hours of daylight in New Orleans in 1994 is given by the function  D(x) =…

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Q: +x 2 1 dx X

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Q: In/cosh(2x)– sinh (2x)): Select one: O 2x None O O

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Q: X 3x2 +5 dx x4

A: To find the indefinite integral and to check the result by differentiation.

Q: 4. Find The coefficient of the x’term in the Maclaurin polynomial for sin(2x)

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Q: V 6² — (x − a)². b) Use a trigonometric substitution to evaluate the indefinite integral. s dx You…

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Q: (ii) Evaluate the definite integral r³e² dr.

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