If f(2) = 4, can you conclude anything about the limit of f(x) as x approaches 2?

बेरीज

No, f(x) = 4, It is the value of the function at x = 2

This limit doesn’t exists at x = 2

Since f(2) = 4

It need not imply that `lim_(x -> 2^-) f(x) = lim_(x -> 2^+) f(x)`

∴ We cannot conclude at x = 2

shaalaa.com

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

पाठ 9: Differential Calculus - Limits and Continuity - Exercise 9.1 [पृष्ठ ९८]

पाठ 9 Differential Calculus - Limits and Continuity
Exercise 9.1 | Q 20 | पृष्ठ ९८

Evaluate the following limit:

`lim_(x -> 2)[(x^(-3) - 2^(-3))/(x - 2)]`

Evaluate the following limit:

`lim_(x -> 5)[(x^3 - 125)/(x^5 - 3125)]`

Evaluate the following limit :

`lim_(x -> 7)[((root(3)(x) - root(3)(7))(root(3)(x) + root(3)(7)))/(x - 7)]`

Evaluate the following limit :

If `lim_(x -> 5) [(x^"k" - 5^"k")/(x - 5)]` = 500, find all possible values of k.

Evaluate the following limit :

`lim_(x -> 0)[(root(3)(1 + x) - sqrt(1 + x))/x]`

In the following example, given ∈ > 0, find a δ > 0 such that whenever, |x – a| < δ, we must have |f(x) – l| < ∈.

`lim_(x -> 2)(2x + 3)` = 7

Evaluate the following :

Find the limit of the function, if it exists, at x = 1

f(x) = `{(7 - 4x, "for", x < 1),(x^2 + 2, "for", x ≥ 1):}`

Evaluate the following :

Given that 7x ≤ f(x) ≤ 3x² – 6 for all x. Determine the value of `lim_(x -> 3) "f"(x)`

If the limit of f(x) as x approaches 2 is 4, can you conclude anything about f(2)? Explain reasoning