-80 If g is a continuous function on [-80, 0] and g(t) dt = V41 Then the value of the integral 22 1+ dx is V41 О 59 O 57 O 58 O 60 O 56

Q: d x4. dx x³J3.a x*J3.b0 X' x³J3c0 x*J4 d O

A: We first write the general form of j_n then we take the derivative of x^4j_4 with respect to x and…

Q: f:1→1, (f(a)), =1 if n = 0 = n-a, – 1 if n= 0 (f(b)), = b, find b2010 - %3D

A: Given: f(a)n=1 if n=0nan-1 if n≠0and f(b)n=bn To find: b2010=?

Q: Prove that •1 to(xt) 1-1² dt = Sinx x

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Q: 2² – 2, a 3 is continuous everywhere. f(z) = O true O false

A: Given: fx=x2-2,  x≤3x+4,  x>3   As we know that; The function will be continuous at x=a when,…

Q: Exercise 4: How many functions f exist such that f'(x) = 3x2 - 6r +3, and (1,-2) is a point of…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: 4. Prove that f(x, y, z) = 2 - 1 x² + y² is continuous in all its domain.

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Q: Expand [× (à × ř)] d dt

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Q: Prove that m-l dx =0 m +n (し+x)" where m,n are both Positive

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Q: xy3 || 73x+1 Let R=[0,1]x[0,1]. dA= R

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Q: 2. Find a function f and a number a such that f(t) -dt = tanx. Give proper reasoning.

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Q: 1 =dx <1 Prove 4 4

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Q: Prove that if f is continuous, then f(t)(x-t) dt = f(u) du ) dt

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Q: show that the function fer fcx)= A - JX Satifl-y 2 the hypo theses of Roll's throrem on

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Q: |х — 1 x5

A: Use the method of substitution to evaluate the integral. I=∫x−1x5dx=∫x−1x52dxLet u=xdu=12xdxSo,…

Q: Evaluate: du S²₁₂ So (x²-y²)²] dt x+y

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Q: prove that ਰ Apply the calculus of residues to dx (1 + x²)² - π 4 .

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Q: 28. Marginal profit. The profit, in thousands of dollars, from the sale of x thousand candles can be…

A: Given query is to find marginal profit at indicated point.

Q: The integral of the given function ſ**-16) x3 3/2 dx is

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Q: For æ > 0, 1 dt 1+t2 A 2/7(1+z) B 2/7(1+JE) c) 1+1 D 1+z E VE

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Q: 11. The function f(x) is defined on [1, o0) and satisfies VTO dt. 10 Find f(x).

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Q: 5. Determine the interval on which f(x) = x+2 is integrable. %3D (-00, 2) [-2, co0) (-00,-2) U (-2,…

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Q: Let f (x) = dt. Find the value of f'(2) 4 -12 8 -24 -4 24 12 -8 100

A: Newton's Leibnitz rule for one variable is as, I(x)=∫ϕ(x)ψ(x)f(t)dtdI(x)dx=f(ψ(x))ψ'(x)-f(ϕ(x))ϕ'(x)…

Q: Let H (2) places. = Z In(z) Compute H'(2.2). Round your answer to 2 decimal

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Q: -2 Evaluate: ²₁²[(x²-²²] 0 x+y du dt

A: Topic = Integration

Q: Q2) Evaluate the integral x3 dx 3 a *0.

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Q: F(x+y=z₁ x² + y²) where 2= z(x,y) Prove that x2² - y2/²/² = x-y dy if it was

A: We have to show that x∂z∂y-y∂z∂x=x-y for the given integral surface of the partial differential…

Q: eſt 2 du given that * f(z) dx = 12 f(4Tan¹(u)) 1+u² Evaluate

A: Hint :  This problem is application method of substitution in definite integral. If you have not…

Q: Find af af Әх' ду af ду f(x, y) = 7(x2 + y2) log(x2 + y2), (x, y) ≠ (0, 0) af Әх for the following.…

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