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SECONDARY
CALCULUS AND ANALYSIS
CALCULUS 1
LIMITS AND CONTINUITY
Secondary
Calculus and Analysis
Precalculus
Calculus 1
Limits and continuity
Derivatives
Integrals
Polynomial graphs
Exponential models
Transformations of functions
Analyzing functions
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Calculus 1: limits and continuity solving
Recent questions in Limits and continuity
Limits and continuity
asked 2021-01-31
Use Taylor series to evaluate the following limits.
\(\lim_{x\rightarrow0}\frac{\sec x-\cos x-x^2}{x^4} \ (Hint: \text{The Maclaurin series for sec x is }1+\frac{x^2}{2}+\frac{5x^4}{24}+\frac{61x^6}{720}+...)\)
Limits and continuity
asked 2021-01-31
Find the limits. Write
\(\infty\)
or
\(-\infty\)
where appropriate.
\(\lim_{x\rightarrow0^-}\frac{x^2-3x+2}{x^3-4x}\)
Limits and continuity
asked 2021-01-30
Evaluate the following limits:
\(\lim_{y\rightarrow0}\frac{1-\cos(7y)}{2y}\)
Limits and continuity
asked 2021-01-27
Find the limit.
\(\lim_{x\rightarrow(\pi/2)}\frac{\sec x}{\tan x}\)
Limits and continuity
asked 2021-01-17
Evaluate the following limits.
\(\lim_{(x,y,z)\rightarrow(1,1,1)}\frac{yz-xy-xz-x^2}{yz+xy+xz-y^2}\)
Limits and continuity
asked 2021-01-16
Find each of the following limits. If the limit is not finite, indicate or for one- or two-sided limits, as appropriate.
\(\lim_{t\rightarrow0}\frac{5t^2}{\cos t-1}\)
Limits and continuity
asked 2021-01-16
Find the limits: As
\(x\rightarrow\infty, \frac{-2x(x^2+4)}{-7-7x^4}\)
Limits and continuity
asked 2021-01-15
Suppose the functions f(x) and g(x) are defined for all x and that
\(\lim_{x\rightarrow0}f(x)=\frac{1}{2}\)
and
\(\lim_{x\rightarrow0}g(x)=\sqrt2\)
. Find the limits as
\(x\rightarrow0\)
of the following functions.
\(f(x)\frac{\cos x}{x-1}\)
Limits and continuity
asked 2021-01-13
Evaluate the following limit.
\(\lim_{x\rightarrow0}\frac{\sin ax-\tan^{-1}ax}{bx^3}\)
Limits and continuity
asked 2021-01-13
Evaluate the following limits.
\(\lim_{(x,y)\rightarrow(1,2)}\frac{\sqrt{y}-\sqrt{x+1}}{y-x-1}\)
Limits and continuity
asked 2021-01-10
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(1,1)}\frac{x^2+xy-2y^2}{2x^2-xy-y^2}\)
Limits and continuity
asked 2021-01-08
Evaluate the following limits.
\(\lim_{x\rightarrow2}\frac{\sin(x-2)}{x^2-4}\)
Limits and continuity
asked 2021-01-07
Find the limit:
\(\lim_{x\rightarrow\infty}\frac{\sqrt{9x+1}}{\sqrt{x+1}}\)
Limits and continuity
asked 2021-01-04
Find the limits:
\(\lim_{x\rightarrow3}f(x),\ where\ f(x)=\frac{1}{2}x-7\)
Limits and continuity
asked 2021-01-04
Find the limit and discuss the continuity of the function.
\(\lim_{(x,y)\rightarrow(3,1)}(x^2-2y)\)
Limits and continuity
asked 2021-01-02
Find the limit:
\(\lim_{x\rightarrow\infty}\frac{3x^6-x^4+2x^2-3}{4x^5+2x^3-5}\)
Limits and continuity
asked 2021-01-02
Use the method of your choice to evaluate the following limits.
\(\lim_{(x,y)\rightarrow(0,1)}\frac{y\sin x}{x(y+1)}\)
Limits and continuity
asked 2020-12-30
Evaluate the following limits.
\(\lim_{(x,y)\rightarrow(e^2,4)}\ln\sqrt{xy}\)
Limits and continuity
asked 2020-12-27
Find the limits:
\(\lim_{x\rightarrow3}\frac{-2}{x-3}\)
Limits and continuity
asked 2020-12-24
Find the limits
\(\lim_{x\rightarrow0}\sin(\frac{\pi+\tan x}{\tan x-2\sec x})\)
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