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: 4. Find two possible non-linear functions & and such that goh= √sinx-x²

A: To find the non linear function by the given composition.

Q: 2. a) Find a formula for f-1 for the function y =f(x) = (x – 2)2 , x< 2 b) Evaluate the expression…

A:

Q: Use the figures to evaluate each function given that f(x)=sinx,g(x)=cosx, and h(x)= tan x. g (2α )

A: We have to evaluate g2α From  the second figure x2+y2=1⇒r=1 ⇒x,y=-14,b ⇒x=-14, y=b⇒rsinα=-14,…

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: Differentiate the given sin (x² +1) 2 X

A: Sin(x2+1) To differentiate the given function

Q: C. lim x→1+ 5x 4 31 -1-x 3x]

A:

Q: Let a<b. Use an important theorem to reason that t  | y(b) − y(a) | ≤ 3000(b − a).  The function is…

A: Step:- 1 Mean value Theorem :- Let f be a continuous function on [a, b] and function is…

Q: 6z* cos (r*) dr-

A:

Q: Find the definition set of the following function F(x)= √ln(sinπx)

A:

Q: Starting with the function f(x) = cos(x), apply any number of shifts, stretches, compressions, and…

A: f(x)=cos(x)Shift right by π2 unitsmx=cosx-π2=cosπ2-x=sinx

Q: Simplify J25 sin² (t) +25c05² (+)

A:

Q: Verify that the following function is harmonic u(x, y) = -ey sin x - 2e siny. Find a harmonic…

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Q: Consider the function f(x) = cos(x2 - 2) + 1 on the interval (-3,3). Calculate the two x-intercepts…

A: f(x)=cos(x2-2)+10=cos(x2-2)+1cos(x2-2)=-1 As we already know, the solution to the trigonometric…

Q: PLS HELP ASAP ON ALL ASKED QUESTIONS

A: The detailed solution is provided below.Explanation:

Q: 1. Differentiate. Do not simplify. а. f(0) = 3cos(0*)sin(0³ – 2) b. f(x) = 4x + 25-x² + 2x-1

A:

Q: a) f(x) = 1+ Sinx b) f(x) = x² + 2x- 1 c) f(x) = 2* + 2 for all x eR for all x eR for all x eR

A: Given function are: [1] f(x) = 1 + Sinx   for all x ∈R [2] f(x) = x2 + 2x - 1  for all x ∈R [3] f(x)…

Q: 3. Determine the exact value of f"(0) for f(x) = (cos5x + 5x²)*.

A: Given

Q: Prove that there is a real number r so that sin(r) = x – 1.

A: We have, sinx=x-1 Let us consider a function fx such that, fx=x-1-sinx

Q: EX: using the relation I= Vn show that J1(x) = 2 sin x

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Q: Evaluate the definite integral 8 sin(x)dr

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Q: The function f is defined by f(x) = x² - 2 - 4 sin (3x² + 5). Let l be the line tangent to the graph…

A: