Let the sequence {fn(x)} be defined on [0, 1] by n Рn2x; if x E (0, ) fn(x) : otherwise SHOW THAT: 1 1 limno | fn(x)dx | limn°fn(x)dx.

Q: х+4 a) Compute lim X3 (x-5)(x-3)

A:

Q: lim (1-e X-

A: Limiting value of function is the value achieved by function when variable tends to approach certain…

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

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Q: Find the limit.

A:

Q: Show that lim Z-2 (2-2)4 || ∞

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Q: Find lim (e* + x³ /2+2x)²/*. 1/x X+ 0+

A: Use log property and then use l hospital's rule to solve the limit.

Q: Show that - lim→∞ Xn = limn→∞(-Xn).

A: The objective of this question is to prove that the limit of a sequence multiplied by a negative…

Q: 10 Find lim x12s 3. X->- X -25 2 lim Jx +3 - 2 メ→」 O lim Sitx - -x 3. 1-X 2 X

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Q: а) If V5 - 2r s f(x)s V5 – x² for -1sxsl Find lim,o f (x) ?

A: Given that                                5-2x2≤f(x)≤5-x2  for  -1≤x≤1 we have to find…

Q: Find lim,00(e3 +2x)/* 1/x

A:

Q: 2 3 ( - 1²/1 ) ² 3 lim 3 X→∞ x

A:

Q: Find the limit as x approaches infinity of (2x-1)(3-x)/(x-1)(x+3)

A: Given query is to find indicated limit.

Q: Find the limit

A: The given expression limx→013+x-13x

Q: Find the lim inf (xn) and lim sup (xn) of Xn=3-(-1)"

A:

Q: Find the limit

A: We have to find the limit of following expression: limx→55-xx2-25 First of all we need to check the…

Q: 72-1402 40+2 o f (x)= [0]. Let f (x) = The lim, ∞

A: We will take x^5 common from numerator and denominator.

Q: limx→00 x3 lim,- is x.

A: Limits

Q: Find the one-sided limit

A: Given: limx→-12+6x2+x-14x2-4x-3

Q: find the limit

A:

Q: Find lim(x-4) (f(x)of the graph below

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Q: 4х — 1 4x2 + 3x - Find lim f(x) if 5. x2

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Q: d) lim (xe”* +1)/ x->0*

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Q: e* - 1 lim VI+x -1 +х — X0

A:

Q: Find lim f (x) if, for all x, 9 cos (4x) <f (x) < 8x2 +9. lim f (x) = %3D

A: The given inequality is: 9 cos(4x)≤f(x)≤8x2+9

Q: Suppose the sequence of numbers o, ₁,...,,... satisfies the difference equation 2k+1=0k+ where a and…

A:

Q: If lim x→0 a) f(x) x = 1 and lim x-0 lim g(x) x→0 g(x) – 2, evaluate: X b) lim x-0 g(x) f(x)

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: lim x3 -1 is x-1- x -1 А. — 3 B. no limit C. 3 D. undefined Е. О

A: topic - limits

Q: x2 – x – 12 lim 2. Evaluat" t→4 3x – V16 – x

A: Limit is the value of the expression as the independent variable approaches certain value, not…

Q: tan(31x) lim x → 0 5x

A:

Q: lim In(10x) x-0t

A: To find the below right-hand limit.

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.