(1) Let f : [0, 1] → R be defined by f(x) = Compute U(Pn, f) and L(Pn, f). x-1 x Qn [0, 1] - X 2 x & Qn [0,1]] n and Pn = }· {0, 1/1, 2/1. n' n' " n

Q: Let r(x) = f(g(x)) and s(x) = g(f(x)), where f and g are shown in the figure. Find r'(1) and s'(4).…

A: our objective is to find the required derivative

Q: Compute r''(t) and r'''(t) for the following function. r(t) = (9t2 + 3,t+ 1,1) = (9r?. Find r'(t).…

A: Find the first, second, and third derivative of the following vector-valued function. r(t) = <9t2…

Q: Let F(x,y,z) = (x)i + (y)j + (z2)k. Compute the defined operations and if it is not defined, write…

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Q: Let X ~ N (0, 1). Demonstrate that E (X)=0 and V (X)=1.

A: To demonstrate that E(X)=0 and V(X)=1 for a standard normal distribution X∼N(0,1), we need to…

Q: 1) Let f(z,y)- . Compute DS(z,y) where u- (4-9)

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Q: Let f(=) = In[=*(z +8)*(z² + 8)°] f'(z) %3D

A: Given that fx=lnx3x+85x2+82 To find f'x

Q: Let T: R³ R² be defined by T (C) X2 - [3²1-22] = -3x3 -3 7 -- {~ - [ ] - - [E] - - [ ]} -- ² - {~ -…

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Q: Theorem: The Chain Rule provided If m(x) = EI(x) is a composite function, then that E'[I(x)) and…

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Q: 2) Let f be a (1:1) Pinction such that differenhable f(3) = 7 P(7) = 8, f'(3)=2, P(1) -3 If glad = f…

A: topic - derivative of inverse function if f(a)=bg(x)=f-1(x)then g'(b)=1f'(a)

Q: A. T(f(t)) = |B. T(ƒ(t)) = f(−t) from Pg to Pg = tª ƒ' (t) from P₂ to P5 = f(t)ƒ' (t) from P7 to P13…

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Q: f (x, y) ~ bo + b1,0(x − 1)+b0,1(y−2)+ b2,0 (x - 1)² + b₁,1(x − 1)(y-2) + bo,2(y − 2)² +…...

A: We find the Taylor series of the given function

Q: K=Zp(t) ,then f(x)=x^p-t is irreducible over K[x]

A: GIVEN: K = Zp(t)

Q: Suppose that f: [1,9] →→ R² such that f(1) =(2,-2) and f' (t) Find f(9) (v₁, 71) √t, √t

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Q: The linear functional F: R^2[x] -> R is defined by the formula F: p -> ∫(from 1 to 0) p(t)dt.…

A: Step 1: Step 2: Step 3: Step 4: