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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

Solutions > EN: pre-calculus-function-periodicity-calculator title >

periodicity of f(x)=cos(2x+5)

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`x`²	`x`^□	log_□	√☐	^□√☐	≤	≥	□□	·	÷	`x`^◦	π
(☐)^′	`ddx`	∂∂`x`	∫	∫_□^□	lim	∑	∞	`θ`	(`f` ◦ `g`)	`f`(`x`)

☐²

x^☐

√☐

^□√☐

□□

log_□

π

θ

∞

∫

ddx

≥	≤	·	÷	`x`^◦	(☐)	\|☐\|	(`f` ◦ `g`)	`f`(`x`)	ln	`e`^☐
(☐)^′	∂∂`x`	∫_□^□	lim	∑	sin	cos	tan	cot	csc	sec

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discontinuity 4x²−36xx−9

Solution

Removable Discontinuity at x=9

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Function points of discontinuity definition

A function f(x) has removable discontinuity at x=a if lim_{x→ a}(f(x)) exists and finite,
but function is either undefined at x=a or lim_{x→ a}(f(x))≠ f(a)
f(x) has step discontinuity if one-sided limits exist and finite but not equal.
f(x) has essential discontinuity if one or both of the one-sided limits don't exist or are infinite.

Find undefined (singularity) points: x=9

Check discontinuity of the singularity points

4x²−36xx−9 at point x=9: Removable Discontinuity at x=9

Removable Discontinuity at x=9

Solve instead

domain 4x²−36xx−9

range 4x²−36xx−9

inverse 4x²−36xx−9

Function Periodicity Examples

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