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Find the limit of $\frac{7x+8}{4x+3}$ as $x$ approaches $\infty $

Step-by-step Solution

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Solution

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Final answer to the problem

$\frac{7}{4}$
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Step-by-step Solution

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of (7x+8)/(4x+3) as x approaches infinity. As it's an indeterminate limit of type \frac{\infty}{\infty}, divide both numerator and denominator by the term of the denominator that tends more quickly to infinity (the term that, evaluated at a large value, approaches infinity faster). In this case, that term is . Separate the terms of both fractions. Simplify the fraction \frac{7x}{x} by x. Evaluate the limit \lim_{x\to\infty }\left(\frac{7+\frac{8}{x}}{4+\frac{3}{x}}\right) by replacing all occurrences of x by \infty .

Final answer to the problem

$\frac{7}{4}$

Exact Numeric Answer

$1.75$

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Function Plot

Plotting: $\frac{7x+8}{4x+3}$

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◻2
◻◻
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◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

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Main Topic: Limits by Direct Substitution

Find limits of functions at a specific point by directly plugging the value into the function.

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