Find the limit of $x^2+3x+\frac{9}{4}$ as $x$ approaches 0

Step-by-step Solution

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Final answer to the problem

$\frac{9}{4}$
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Step-by-step Solution

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The limit of a sum of two or more functions is equal to the sum of the limits of each function: $\displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x))$

$\lim_{x\to0}\left(x^2\right)+\lim_{x\to0}\left(3x\right)+\lim_{x\to0}\left(\frac{9}{4}\right)$

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$\lim_{x\to0}\left(x^2\right)+\lim_{x\to0}\left(3x\right)+\lim_{x\to0}\left(\frac{9}{4}\right)$

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Learn how to solve limits by direct substitution problems step by step online. Find the limit of x^2+3x9/4 as x approaches 0. The limit of a sum of two or more functions is equal to the sum of the limits of each function: \displaystyle\lim_{x\to c}(f(x)\pm g(x))=\lim_{x\to c}(f(x))\pm\lim_{x\to c}(g(x)). The limit of a constant is just the constant. Evaluate the limit \lim_{x\to0}\left(x^2\right) by replacing all occurrences of x by 0. x+0=x, where x is any expression.

Final answer to the problem

$\frac{9}{4}$

Exact Numeric Answer

$2.25$

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Function Plot

Plotting: $x^2+3x+\frac{9}{4}$

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0
a
b
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g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
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

How to improve your answer:

Main Topic: Limits by Direct Substitution

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

Used Formulas

See formulas (1)

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