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What math levels does Goblins cover?

Goblins covers math from Grade 5 through AP Calculus, including thousands of standards-aligned topics. Teachers can also upload their own content for custom assignments at any level.

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MA.CF.2.e.iv

determine the limit of a function from a given graph.

Example Problems

The function k is defined over the real numbers. This table gives a few values of k.

x	k(x)
-0.1	-3.09
-0.01	-3.01
-0.001	-3.001
0.001	-2.999
0.01	-2.99
0.1	-2.9

What is a reasonable estimate for

\lim_{x \to 0} k(x)

The function r is defined over the real numbers. This table gives a few values of r.

x	$r(x)$
1.9	-8.12
1.99	-8.02
1.999	-8.001
2.001	-7.999
2.01	-7.98
2.1	-7.88

What is a reasonable estimate for

\lim_{x \to 2} r(x)

The function

w

is defined over the real numbers. This table gives a few values of

w

x	w(x)
6.9	2.89
6.99	2.99
6.999	2.999
7.001	3.001
7.01	3.01
7.1	3.11

What is a reasonable estimate for

\lim_{x \to 7} w(x)

Khan Academy Resources

Limits intro Limits and continuity: FAQ Estimating limit values from graphs Limits of combined functions: sums and differences Infinite limits: graphical Limits of combined functions: products and quotients One-sided limits from graphs Estimating limit values from graphs Limits of composite functions Limits intro Limits at infinity: graphical Connecting limits and graphical behavior Introduction to infinite limits One-sided limits from graphs Infinite limits and asymptotes Connecting limits and graphical behavior Introduction to limits at infinity Limits of composite functions: external limit doesn't exist Limits of composite functions: internal limit doesn't exist Theorem for limits of composite functions: when conditions aren't met Limits of combined functions: piecewise functions Estimating limit values from graphs One-sided limits from graphs: asymptote Theorem for limits of composite functions Unbounded limits Limits of combined functions

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