Find lim h→0 (a + h)² − a² h O a O b Ос Od 0 does not exist a 2a

Q: Evaluate the following limits: 1-cos¹(x) (i) lim zsin(2x) (ii) lim In (√) +1 2²-1 (iii) lim sin(x) -…

A: Given :limx→01-cos4(x)sin(2x)lim x→1 lnxx2-1lim x→π4 sinx-22cosx-22lim x→01+tan(2x)1x

Q: 3. Let f(2) = if z + 2i, while f(2i) = 3+4i, is f(2) continuous at z = 2i? 2- 2i 4. Evaluate lim (az…

A: 3)Given:

Q: Find the limits lim(2 - 3 as 1/3 a. t→0* b. t-0

A: Given function is: ft=2-3t13 As t→0+ we get, limt→0+ft=limt→0+2-3t13=2-∞=-∞

Q: lim x16 x → 0 x2 – 2sinx +2x O 272 O 240 о 1

A: we will solve this using L'Hospitals rule.

Q: |4x – 12| lim Compute x→3- x – 3 -

A:

Q: Compute when: = (a) Zn in! + 2-n (b) ²n = 2-n+i√n Zn (c) Zn n √z, for z € C lim Zn n→∞

A:

Q: Find the limit. За + 5 lim x→0 x – 4 O -5/4 O DNE O 3

A: Limit problem

Q: 12. Given f(x)=x² – 4x – 5. Find lim fx) –{2) x-2 2

A:

Q: V5x+4-3 3) lim X-1 x-1

A:

Q: Prove lim(Vn+1- n)=c 8. 0 =

A:

Q: 2x² + x – 1t lim x→-1 x + 1

A:

Q: t3 + 3t2 - 12t +4 lim t→2 t3 – 4t

A: Given,          limt→2t3+3t2-12t+4t3-4t

Q: Let f(x) = ⌊x⌋ + ⌊−x⌋ where ⌊x⌋ is the least integer function i.e. for a given input x it returns…

A: Given that,fx=x+-x   ,   where -x is the least integer function. f2=2+-2      =2+-2…

Q: Complete the proof that lim (-2x − 4) = -10 by filling in the blanks. Use "e" for & and "d" for 8.…

A: We have to complete the proof that limx→3 (-2x-4) = -10  by filling in the blanks.

Q: 5x+4 lim X=-0 V9x2 –1 X =00

A: Consider the limit: limx→-∞5x+49x2-1 Expand the fraction:…

Q: C. lim (4x xx-√16x² + 3x - 5) X→∞

A: Given limits, (c) limx→∞4x-16x2+3x-5 (d) limx→03x-7x2x-15x We have to find the Limit of the given…