Evaluate the following limits 1-e²x)² 7x (a) lim- x-0 1-cosx (b) lim x² In 1 *** 1 9x²

Q: 3n Find lim,→0 (1+ )'

A: Here,

Q: x' - 4x? – 9x+36 lim b) x - x-12 x-3 e* -e* – 2x lim c) x- sin x

A: limx→-3x3-4x2-9x+36x2-x-12=limx→-3x2x-4-9x-4x2-4x+3x-12=limx→-3x2-9x-4xx-4+3x-4=limx→-3x2-32x-4x-4x+…

Q: Suppose lim f1x2 xSa o and lim glx2 = ". Prove that xSa %3D lim 1f1x2 + glx22 xSa

A:

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

A:

Q: Find the limit

A:

Q: UESTION 13 The integral test can be used to determine whether or not E, =1 1 converges. O True o…

A: Since you have asked multiple question,as per our guidelines we are supposed to answer only one…

Q: Determine lim X- • ot s/x 7 Sinx

A: limx→0+5x-7sinx

Q: Calculate 14. lim (√x² + 1 - x). X18

A: Using series expansion about x =inf

Q: Find the limit

A: Given limit expression islim△x→0x+△x3-x3△x.

Q: Determine the 3z 1 2x 1 2x 5 lim 00 O 00 2/4

A:

Q: lim (x)¹/(2x) €→∞

A: Note:- Since you asked multiple questions ,according to our policy we can solve only first question…

Q: 1– x2 lim r--00 3 + 2x – x3

A:

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

A:

Q: e* - 1 lim VI+x -1 +х — X0

A:

Q: 2 In x lim x→+∞

A:

Q: 4/2+81x 3 X→∞0 X +7 Find lim lim X→∞0 2+81x 3 X +7 = (Simplify your answer.)

A: Given query is to find indicated limit.