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Find the limit $\lim_{x\to4}\left(\frac{x^4-256}{x-4}\right)$

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Solution

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Final Answer

$256$
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Step-by-step Solution

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Factor the difference of squares $x^4-256$ as the product of two conjugated binomials

$\lim_{x\to4}\left(\frac{\left(x^{2}+16\right)\left(x^{2}-16\right)}{x-4}\right)$

Learn how to solve differential calculus problems step by step online.

$\lim_{x\to4}\left(\frac{\left(x^{2}+16\right)\left(x^{2}-16\right)}{x-4}\right)$

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Learn how to solve differential calculus problems step by step online. Find the limit (x)->(4)lim((x^4-256)/(x-4)). Factor the difference of squares x^4-256 as the product of two conjugated binomials. Factor the difference of squares \left(x^{2}-16\right) as the product of two conjugated binomials. Simplify the fraction \frac{\left(x^{2}+16\right)\left(x+4\right)\left(x-4\right)}{x-4} by x-4. Evaluate the limit \lim_{x\to4}\left(\left(x^{2}+16\right)\left(x+4\right)\right) by replacing all occurrences of x by 4.

Final Answer

$256$

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Limits by Direct SubstitutionLimits by L'Hôpital's ruleLimits by FactoringLimits by Rationalizing

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Function Plot

Plotting: $\frac{x^4-256}{x-4}$

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0
a
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n
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x
y
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(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
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: Differential Calculus

The derivative of a function of a real variable measures the sensitivity to change of a quantity (a function value or dependent variable) which is determined by another quantity (the independent variable). Derivatives are a fundamental tool of calculus.

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