In exercise problems 7 - 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why? limx→3(4-x)

In exercise problems 7 – 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why?

`lim_(x -> 3) (4 - x)`

आलेख

From the graph the value of the function at x = 3 is y = f(3) = 1

∴ `lim_(x -> 3) (4 - x)` = 1

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अध्याय 9: Differential Calculus - Limits and Continuity - Exercise 9.1 [पृष्ठ ९६]

अध्याय 9 Differential Calculus - Limits and Continuity
Exercise 9.1 | Q 7 | पृष्ठ ९६

Evaluate the following limit:

`lim_(z -> -5)[((1/z + 1/5))/(z + 5)]`

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 :

`lim_(x -> 0)[((1 - x)^8 - 1)/((1 - x)^2 - 1)]`

In exercise problems 7 – 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why?

`lim_(x -> 5) |x - 5|/(x - 5)`

In exercise problems 7 – 15, use the graph to find the limits (if it exists). If the limit does not exist, explain why?

`lim_(x -> 1) sin pi x`

Sketch the graph of f, then identify the values of x₀ for which `lim_(x -> x_0)` f(x) exists.

f(x) = `{{:(sin x",", x < 0),(1 - cos x",", 0 ≤ x ≤ pi),(cos x",", x > pi):}`

Sketch the graph of a function f that satisfies the given value:

f(0) is undefined

`lim_(x -> 0) f(x)` = 4

f(2) = 6

`lim_(x -> 2) f(x)` = 3

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