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Limit of the function
:
Limit of (3-3*x^2+4*x^4+6*x^3)/(2*x^2+7*x^4)
Limit of ((5+4*x)/(-1+5*x))^(1+3*x)
Limit of (1+x^3-2*x)/(8+x^10-9*x)
Limit of x^2+a/(x^3-a^3)-x*(1+a)
Derivative of
:
4*sqrt(x)
Integral of d{x}
:
4*sqrt(x)
Identical expressions
four *sqrt(x)
4 multiply by square root of (x)
four multiply by square root of (x)
4*√(x)
4sqrt(x)
4sqrtx
Similar expressions
4*sqrt(x^2)
Limit of the function
/
4*sqrt(x)
Limit of the function 4*sqrt(x)
at
→
Calculate the limit!
v
For end points:
---------
From the left (x0-)
From the right (x0+)
The graph:
from
to
Piecewise:
{
enter the piecewise function here
The solution
You have entered
[src]
/ ___\ lim \4*\/ x / x->16+
$$\lim_{x \to 16^+}\left(4 \sqrt{x}\right)$$
Limit(4*sqrt(x), x, 16)
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
Plot the graph
Rapid solution
[src]
16
$$16$$
Expand and simplify
One‐sided limits
[src]
/ ___\ lim \4*\/ x / x->16+
$$\lim_{x \to 16^+}\left(4 \sqrt{x}\right)$$
16
$$16$$
= 16.0
/ ___\ lim \4*\/ x / x->16-
$$\lim_{x \to 16^-}\left(4 \sqrt{x}\right)$$
16
$$16$$
= 16.0
= 16.0
Other limits x→0, -oo, +oo, 1
$$\lim_{x \to 16^-}\left(4 \sqrt{x}\right) = 16$$
More at x→16 from the left
$$\lim_{x \to 16^+}\left(4 \sqrt{x}\right) = 16$$
$$\lim_{x \to \infty}\left(4 \sqrt{x}\right) = \infty$$
More at x→oo
$$\lim_{x \to 0^-}\left(4 \sqrt{x}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 \sqrt{x}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(4 \sqrt{x}\right) = 4$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 \sqrt{x}\right) = 4$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(4 \sqrt{x}\right) = \infty i$$
More at x→-oo
Numerical answer
[src]
16.0
16.0
The graph