Let ƒ be defined on a neighborhood of xo. Show that if ø is defined on a neighborhood of to and continuous at to with x = ¢(t) and xo = ¢(to) then lim f(x) = lim f($(t)). tto

Q: a) Find the limits of the following functions: i. sin 2x lim o 2x +x V+ 12-4 lim X-2 x- 2

A: To find the limits of the following functions : (i)  limx → 0 sin 2x2x2 + x(ii)  limx → 2 x2 + 12…

Q: Let f be defined on a neighborhood of xo. Show that if ø is defined on a neighborhood of to and…

A: Given: f is defined on a neighbourhood of x0 and ϕ is defined on a neighbourhood of t0 and…

Q: Let ce (a, b). If ƒ (x) is a function that is continuous at c, then lim,e- [f (x)] = lim,»c+ [f…

A:

Q: 7. What is the value of (X-2)2 for the scores 2,3,5?

A: To find : ∑X-22 for the scores 2, 3, 5

Q: (4) Let f(x) be the function whose domain is all of R given by the rule 42 if r € Z and f(x) = 10…

A:

Q: Is the secant function even, odd, or neither? Is its graphsymmetric? With respect to what?

A: The given function is secant function y=secx

Q: Q.4: (A) Show that Lim t'i = 4 i t >2

A: The given symbol is the symbol of the limit of the function at the given point of limit.…

Q: Find Lim as x approaches 0 of the function cos(4x-1)/2x

A: Given: limx→0cos4x-12x To find:  The limit limx→0cos4x-12x

Q: If f(x+ y)= f(x)f (y) for all x, y eR and f (x)=1+g(x)G(x), where lim g (x)=0 and lim G (x)…

A: The problem has been solved in detail in the next step.

Q: lim 극 et – 1 x-1

A:

Q: kpression for "12 times x."

A: Times means multiplication. Sometimes it is denoted by dot.

Q: Evaluate the limit lim f(t) where ƒ(t) = = lim f(t) = i 00-11 00-11 (9+17) 2 for t = 0.

A:

Q: I if X > 4 and J (X). 4X + 1 i1 X<4. Find lim f(x) x→4+

A: Given; f(x)=√x-1 if x&gt;4 and f(x)=x2-4x+1 if x&lt;4.

Q: Evaluate the limit (1 – cos x)² sin² . lim x2(1 – e)4 COS X - -

A: Given limit is : limx→01-cosx2sin2xx21-ex4  To find the value of the limit.

Q: Suppose that f is a function that is continuous at a number c. Which of the following statements I,…

A: The function f is continuous at a number c.

Q: Give a pair of functions f: R →R and g : R →R such that g is not tangent to f at 0 and yet lim,0…

A: To give a pair of function f : ℝ→ℝ and g : ℝ→ℝ such that g is not tangent to f at 0 and yet limx→0…

Q: If f: Z → R is a function, then the expression lim f(x) is undefined. x-2 True False

A: If f:ℤ→ℝ, is a function then  limx→2f(x) is undefined. To Check: Whether the given statement is true…

Q: Let ƒ : D → R be a function and let xo be a limit point of D that also belongs to D. Show that the…

A:

Q: Use the graphs of f and g and their tangent lines at (2, 0) to find lim f(x) x+2 g(x) y 1 -1 -2 y =…

A: By using the graphs of  and their tangent lines at  to find .