Show that if lim(a /n) = L, where L > 0, then lim(a,) = +0o.

Q: is it true that ∇f(limx)=lim∇f(x) and further that ∇2f(limx)=lim∇2f(x)?

A: We know,  ∇f(xi)=f(xi)-f(xi-h), h=xi-x0i,i=0,1,2...And…

Q: . Use the Squeeze Theorem to determine the value of limx sin

A: To evaluate the given limit limx→0x4sinπx by using the Squeeze theorem. Now, the Squeeze thorem…

Q: 5. Use L'H rule to find (a). lim Inz2 (b). lim (sin x)(In x).

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.