Question

Calculate each limit below, if it exists. If a limit does not
exist, ** explain why**. Show all work.

\lim _{x\to 3}\left(\frac{x-3}{\sqrt{2x+3}-\sqrt{3x}}\right)

\lim _{x\to -\infty }\left(\frac{\sqrt{x^2+3x}}{3x+1}\right)

Answer #1

Happy to help

Find the limit if it exists or show that the limit does not
exist.
lim (x,y) to (0,0). y^2 sin^2x/ x^4+y^4

Determine each limit or explain why the limit does not
exist.
(a) lim(x,y)→(5,4) : (x − y − 1)/(√(x − y) − 1)
(b) lim(x,y)→(0,1) : (sin(x^(2) + y − 1))/(5y + x^(2) − 5)
(c) lim(x,y)→(3,2) : (4x + y)/(2x − 6)

Find the limits, or state that the limit does not exist (you
must justify answer):
a) \lim_(x->\infty )(\sqrt(x^(2)+2x)-\sqrt(x^(2)-x))
b) \lim_(x->\infty )(lnx-ln(sin x))
c) \lim_(x->\infty )x^((1)/((lnx)))

f(x,y) = (x^4-y^2) / (x^4 + y^2). show the following limit does
not exist, and explain why lim (x,y)->(0,0) f(x,y)

Find the limit, if it exists. (If an answer does not exist,
enter DNE.)
lim (x, y)→(0, 0)
x2 + y2/square root (x2 +
y2+ 25)-5

MY NOTES
Determine the limit of the trigonometric function (if it
exists). (If an answer does not exist, enter DNE.)
lim x→1/2 4x2 tan
πx

please show all work Evaluate each of the following limits, for
after lim the part with x-> and then a number is below the lim
and then after is the fraction part
1) lim x->3 (x^2-2x-3/x^2-5x+6)
2) limx->2 (x-2/square root(2x)-2)
3) lim x->inf (3x^5-7x^3/-5x^5+x^3-9)

Consider the function given byf(x, y)
=((y^2−2^x)/(2x^2+y^2))^3.Show that lim(x,y)→(0,0)f(x, y)does not
exist by computing the limit along the positivex-axis and the
positivey-axis.

Explain why a limit does not exist when x approaches to 2 for
f(x) = √2 − x

Let f(x)=7x^2+7. Evaluate
lim h→0 f(−1+h)−f(−1)/h
(If the limit does not exist, enter "DNE".)
Limit =

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