Give the following infinite sum and limit: 8 2n-1 3n+2¹ n=4 a) rsin r (b) lim 20 x² + e²-1

Q: sin 04) find limx-2n 2x-4n S0 (x²+x+1)* Q5) lim- (r²+1)100

A: In the given question we have to find the limit of the question 4 and question 5. the question 4 is…

Q: Find the limit lim (8x² – 53x4) (822 – 53x)= Click for List

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Q: Deduce that

A: To prove that                limn→∞nn2n!=0

Q: Evaluate using the identity a3 - b3 = (a-b)(a2+ab+b2)

A: Given limit limx→3 x3-27x2-9 We can write the above limit as limx→3 x3-27x2-9=limx→3 x3-33x2-32

Q: mx + 1 1 Find m if lim x +2 x² + 1 O 3 O 2 O 1

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Q: lim (412 + 8t – 5)3/2 t- 2.

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Q: n+1 2n +3 lim 2n +1

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Q: 2x³-x+1 2x² +5x+12 What is lim X-00 2x² -?

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Q: (4-x2) 3-1x2+5 tim

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Q: Lim a 2.

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Q: Evaluate using the identity a3 - b3 = (a-b)(a2+ab+b2)

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Q: lim V8+X -2

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Q: +1 limx0 t2+1

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Q: t-15 - 3t + 45 Find lim Nt +85 –10 -t+15

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Q: lim n2 + 1 n2 + n2 n2 + 4

A: The given limit is: limn→∞nn2+1+nn2+4+...+nn2+n2 so, it can be written as: limn→∞ ∑r=1nnn2+r2

Q: lim 19th 3. 1/-

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Q: 3n + 2 Calculate lim V7n? +1 n00

A: The solution is 37

Q: x²-1 X If lim x0 x+1 - ax - b} = 2, Find the values of a and b.

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Q: |z+3| Find lim z+3 |z+3| lim z+3

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Q: Find the limits

A: Consider the given limit, limn→∞1n+1+1n+2+⋯+12n now write the limit in the summation form,…

Q: Find lim 1 2/3 X 2 (x-4)2/3 as

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Q: Evaluate lim v9x² – 5x + 3x x - 00

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Q: Is it possible to find numbers a, b and c so that an lim n+0o bn3 + cn erists but not equal to 0?…

A: Consider the function:

Q: Evaluate lim ー1 3n+5

A: Given find  limx→∞x2-13x+5

Q: 4x-x2 lim- x4X- 12 O 16 O 13 O 11 O

A: From the given problem:u   limx→44x-x2x-x   So,   limx→44x-x2x-x=4· 4-424-4=16-164-2=02=0

Q: 1 4 lim X + 2* х-2 In(2x-3)

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Q: Evaluate: 2-3х lim (3— г)? - a) 0 b) -00 c) 3 d) +∞

A: Hence option (b) is correct.

Q: If lim (a.) 2 (b.) 4 L(C.) 16 (d.) 64 1+ cx 4, then lim (1+2cx 1-2cx, IS

A: The given limit is: limx→01+cx1-cx1/x=4. To Evaluate: limx→01+2cx1-2cx1/x.