For f in L'[a,b], define. ||f|| = √² x ² | f(x) | dx. Show that this is L' [a,b]. on a norm

Q: Use this definition to find f'(a) at the given number a. f(x) = V5x + 1, a = 3

A: First we find out f'(x) then put x=a=3 in f'(x).

Q: If f:X → Y is a bijective function,-3 then (f^(-1)•f)(x)=(fof^(-1) )(x), XEA

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Q: SUppose F(x) = dt. Find the formda 13 F (x ³) expressed using an integral. ? F (x* )= ]

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Q: Let f(x) = x²+| a.) compute f '(Xbilgebraically b.)use the answer to evaluate f '(3)

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Q: Find the length of the hyperbolic function y = cosh x from (0,1) to (8, cosh 8)

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Q: If f is concave up, then f' is (choose one): (a) increasing. (b) decreasing.

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Q: Find the interval(s) wheref (x) =vx+ 2x+6 jis continuous. A) [2, 6] B (-*, *) C) -6, 6] D) [0, -)

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Q: Prove f-1(E U F) = f-\(E) U f-1(F)

A: We have to prove that f−1E∪F=f−1E∪f−1F. Let x∈f−1E∪F hence, x∈f−1E∪F⇔fx∈E∪F…

Q: 8.. If L' { f(p)} = F (t) then L1 {f( ap) } is : a) aF(at) b) F (t/a) c) F(at) d) (1/a)F (t/a)

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Q: Consider a quadratic function f(x) = ax?+ bx + c, where a, b, CER and a # 0. She hat the tangent…

A: f(x)=ax2+bx+climit definition of derivative states that :f'(x) =limh→0f(x+h)-f(x)hf'(x) =limh→0…

Q: Consider the three basic vectors: (2,1,0,-1),(-1,1,1,1),(2,7,4,1) a. give two vectors that are in…

A: Given the three basic vectors:                           (2,1,0,-1),(-1,1,1,1),and (2,7,4,1) We have…

Q: What would be an example of a function that is not integrable on [2, 10] and why is it not…

A: Consider a function: y=1x-2……1

Q: If you need to prove that a ∈ f^−1 (Y ), what do you need to show?

A: Here we need to show the way to prove a∈f-1(Y)

Q: Show that if f (x, y, z) = 0 then = -1.

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Q: af ?x of ду = = af * \f f(x, y) = C(xy)", with \xy| < 1, find and af = : ду n=0 #

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Q: Suppose f" () > 0 on some interval (a, b). Check all of the following statements that must be true.…

A: Step 1: Let write the given .We are given that f"(x)&gt;0 on some interval (a,b). Step 2: Let write…

Q: {(u)= (u² -3)*

A: Given the function is  f(u) = 12u2-32. We have to find f'(u).

Q: Check the following functions if Piz) exist not and find f'(z) if exist: ,or D fcz) = 1Zit %3D

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: Verify that f has an inverse and find fle) = x'+l; cza

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Q: Please just do 1(b)

A: To compute the required value , by definite integral

Q: Suppose that S(m)3(4#-4)*(32+ 1). Find f'(#), and then evaluate f' at # = 1 and # = -1 (1)= 1(-1)=

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Q: For each of the following functions, find (∂z)/(∂x) and (∂z)/(∂y) (d) If z =…

A: Given: z=ax+by2+eax+by+sinax+by To find: ∂z∂x and ∂z∂y To show: b∂z∂x=a∂z∂y

Q: Use right hand rule to find area under the curve   f(x)= x2-x on interval [1,3]

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Q: 1. v₁ = (4, −2, 6, −4), V₂ = (6, −3, 9, −6)

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Q: Show that if F: AB and G, H F"" (GUH) = F"" (G) U f" (H) and F" (Gn H) = F²¹ (6) ^ F-1 (H) are…

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Q: Find the value(s) of c guaranteed by the Mean Value Theorem for f(x)= x^3-x-1 on [-1,2]. Sketxh the…

A: From the mean value theorem, if the function y=f(x) is continuous in the interval [a,b] and…