3. Given Ln express the limit as n → ∞ as a definite integral, that is provide a, b and f(x) in the expression | f(x)dx.

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A: ∫-33f(z) dz = 0  ,    ∫-35 f(z) dz   = 5find -∫356f(x) dx∫abf(x) dx    = ∫acf(x) dx   +∫cb f(x)…

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Q: Express the limit as a definite integral on the given interval. lim > n- 00 eši . Δχ [0, 8] 5 + Xi i…

A: Given: limn→∞ ∑i=1nexi5+xi∆x,   0,8. To Show: Express the limit as a definite integral on the given…

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A: As per the guidelines, we are supposed to answer only one question at once. Kindly repost the other…

Q: Find lim e x2 dt X 00 0. ej

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Q: +00 dx d.x (1+x)/x

A: Given: To show: The given integral converges.

Q: VI. Suppose h' is continuous at x = 0 and h'(x) =tan(2x) - 1 if x > 0. Find h(0), if it exists.

A: Let's find.

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Q: Let f(x) = x ln(1+ x*). For all æ € [-1, 1], it is known that In(1 + x) = (-1)" -xn+1 n +1 n=0 2.…

A: Substitute x3 for x in the given power series of ln1+x and simplify.…

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Q: 4 1 : Evaluate the following improper integral by using proper limit notations: dx. (4 – x)2/3

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Q: 1. Write the following improper integral as a limit. x-3x In(x)-1 dx x (x-1)

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Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: given,         limx→∞x3e2x

Q: Which of the following correctly expresses the limit lim n5 as a definite integral? А. x* dx В. x°…

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Q: - if f(x) is a continuous function at x O, then a = 1-cos4x よく0 x? { a If f(x) = r= 0 r>0 V16+ VF -

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Q: 1)Differentiate the following f(x) = x³In (3x² – 2x + 7) e sin (x) g(x) = %3D x² – 1 h(x) = log,(x +…

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Q: The limit n lim E /2x + (x; )²Ax i=1 can be expressed as a definite integral on the interval [1, 8]…

A: Concept used: Definition of definite integral is given by ∫abf(x)dx=limn→∞∑i=1nf(xi)△x…

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Q: The limit n lim E V2x; + (x; )²Ax can be expressed as a definite integral on the interval [1, 8] of…

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Q: | 45. Apply integration to the expansion 00 =E(-1)"x" = 1- x+x – x +.. 1+x n=0 to prove that for -1…

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A: 7.  limn→∞∑i=1n2+3in2+3in2+4.3n=12ln268

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Q: a In(1-x) X lim a-1 So dx

A: We can solve this using series then integral

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A: We have to find the value of E.

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A: Q2. It is given that,f(x)=xsin(1x) has a limit at x0 not equal to 0.

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Q: The limit lim e 1+i i=1 n00 can be expressed as a definite integral on the interval [1, 5] of the…

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Q: Use L’Hôpital’s Rule to determine the comparative rates of increase of the functions f (x) = xm,…

A: Consider the limits:

Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

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Q: Given Ln= 2 ²2 Σ [5 (5 + (1 - 1) ² ) ² - 3 (5 + (1 - 1) ²2)]. i=1 definite integral, that is provide…

A: Given Ln=2n ∑i=1n55+i-12n3-35+i-12n4   To Express: The limit as n→∞ as a definite integral, that is…

Q: 4. Given the function f (x) = x³ ln x. Determine the following: e. Horizontal Asymptote(s) using…

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