Man of X = Avenge f= ELK) H.w prove that E (x-x) =0 Hint 又=E(x)

Q: x if x20 If Ax) = -x2 then f'(0) if x <0

A: Given function, fx=x2      if x≥0-x2   if x&lt;0

Q: True or False: If fe L'(T), then {f(n)} € {(T). Fill in the Blank: If " g(x)2 dr < 4, then l@(n)²<

A: Given that, f∈L4(T) Then this can be written as, f=∑n=1∞|an|4 By using the cauchy method, f(n)∈l2(T)…

Q: -1 if f(x) = xtan ,"x,find f' (/3 )by first principle

A:

Q: If f(x) = 6*, then f"(x) = A 6*(In6)3 B 6*(In6) (c) 6* 66 D (In6)3

A:

Q: Let f(x) = 2x e¯x*,x > 0 and Let Y x2. Find G(y)and g(y). %3D

A: In this question,  we need to transform the variable in the probability density function.

Q: Find f. f"(x) = x-2, x > 0, f(1) = 0, f(4) = 0 (x) = -In(x)+ (In(4))x – In(4)

A: Given

Q: Prove that if F(s) = L{f(t)} then L{t" f(t)} = (-1)" d"(F(3)) ds

A:

Q: 6 f(x) = 7 + find f'(x). Find f'(2).

A: As we know that: The sum/difference rule: f±g'=f'±g' The Power law: ddxxn=nxn-1 Given: fx=7+6x+2x2

Q: If f(x) = 3 tan 1 x, then find the value of f'(5) is . %3D -5 26 3 26 3 26 26

A:

Q: 5. If fx) = ene0", find f"(0). a. e b. 1 C. 7 d. 0

A: Derivative

Q: Find f(") (x) given f (x) = In(x + 1)

A: Given function is  f(x) = ln(x+1)  We have to find the nth derivative of f i.e. fn. We use  notation…

Q: If iz' +:-:+i = 0, then show that E=1.

A: iz3+z2−z+i=0   ⟹iz3+i2z+z2+i=0   ⟹iz(z2+i)+(z2+i)=0   ⟹(z2+i)(iz+1)=0   ⟹(z2+i) i (z−i)=0   ⇒z2=−i…

Q: (a) Use the definition of L{·} to determine L{te=#}

A:

Q: Q3) Find the derivative of y for all functions the following (1) y = 0 (sin (In 0) + cos (In 0)),…

A: Since you have posted multiple questions, we have solved the first question for you, if any specific…

Q: 7) Let f(x) be a function such that f(1) x E [1,6]. Find how small can f (6) possibly be? Explain.…

A: We have

Q: 22. State True or False. Let f(x)=sin'(x) + log(x) then domain of f(x) is (-*, ). a) True b) False

A: To check whether the statement is true or not. The statement is Let f(x)=sin2x+logx then domain of…

Q: If limit t y = f(x) write an expression for the differentia dy

A: Given: y=f(x)

Q: Find f ogohif f(x) =, g(x) = x", h(x) = x + 3. 10 x+1'

A:

Q: *+ 3x² + 2 If f(x) = then f'(1) = 0 3 O 7

A: Differentiate wrt x

Q: p(t) = 1 √√/t²

A: Here we have to find the anti derivative i,e integration of p(t)Given p(t)=1t23or, p(t)=t-2/3

Q: Let f(x) = Find f'(x). (x + sec(x³ + 4))*

A:

Q: 8 x + 6 Let f(x) = x + 1 f'(x) =

A: The function is fx=x+6x+18. Find the derivative of the function using the chain rule and quotient…

Q: If 4 – cosh a f(x) 3 + cosh x then f'(x)

A: Given function

Q: - 3 Let f(x) = 8xVæ + x2. f'(x) =

A: Use the derivative for finding the answer.

Q: 3. Differentiate. x²e* f(x)%3= x² + ex

A:

Q: S(x) 르 arcsin (금x + 1) -3 Let f '(x) = . a Find f' (x) giving your answer in the form TV (bx(x + c)…

A:

Q: Find the derivative y = e* In x In x ex E + e* In x O None of these

A: Use product rule:-

Q: 03: Let S(x)=12-x-1|-1. -1. Find f"(0) and Find f'(4)

A:

Q: 7. Find the intervals of increasing/decreasing for the function f(x) = x'e*

A:

Q: 7 x + 3 Let f(x) = x³ . x + 5 f'(x) =

A:

Q: 3 5. If f(x) = and g(x) = 4*, find: X-4 a) f-¹(g(x)) b) the domain and range of f-¹(g(x))

A: