limit as x approaches infinity of (4x-7)/(x^2+5x)

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

☐²

x^☐

√☐

^□√☐

□□

log_□

θ

∞

∫

ddx

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

simplify solve for inverse tangent line

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∑_x=1^∞cos(x)x²

Solution

converges (absolutely)

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Solution steps

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∑_n=1^∞cos(n)n²

The series has positive and negative elements, check for conditional/absolute convergence

Absolute/conditional convergence definition

Absolute Convergence: ∑a_n is absolutely convergent if ∑|a_n| is convergent
Conditional Convergence: ∑a_n is conditionally convergent if ∑|a_n| is divergent and ∑a_n is convergent

Check convergence of ∑_n=1^∞|cos(n)n² |: converges

=converges (absolutely)

Solve instead

∑_x=1^∞cos(n)n²

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−▭▭	<	7	8	9	÷	`AC`
+▭▭	>	4	5	6	×	☐☐☐
×▭▭	(	1	2	3	−	`x`
▭ \|▭	)	.	0	=	+	`y`

limit as x approaches infinity of (4x-7)/(x^2+5x)

Solution

Solution steps

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