9. Evaluate (a) limx→1 2023_ (b) limx→0 x-1 x-sin x ¹x0 4x5-2x³ (c) lim₂-0 3-1-1-2 2x4-3x³

Q: limx→0  (x^2+3) / (1−cosx)

A: given example is, limx→0x2+31-cosx

Q: sin(51x) lim 16x

A:

Q: 1 Evaluate lim Gnx x→1+ 'Inx х-1

A:

Q: What are limx→+-∞ k (k a constant) and limx→+-∞ (1/x)? How doyou extend these results to other…

A: limx→af(x)=L means f(x) becomes arbitrarily close to L as long as x is sufficiently close to a.  We…

Q: 23) lim (5x- 1) = 19 X4

A:

Q: lim y approaches -3 .............. (5 - y)^4/3

A: We have to find the limit: limy→-35-y43 This is determinate form of the limit so we just have to put…

Q: 1 4. Find limx→0+ ( ) ex-1

A: Given :          limx→0+1ex-1-1x

Q: Show that limx-->0+ xlna/1+lnx = a, using L'Hopital's Rule. Show that limx-->∞ xlna/1+lnx = a,…

A: L'hospital's rule -If  is of the indeterminate form of  thenDifferentiation formulas,Log properties,