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Can I use my own voice with Goblins?

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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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Does Goblins support English Language Learners?

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MA.912.C.1.1

Demonstrate understanding of the concept of a limit and estimate limits from graphs and tables of values.

Example Problems

Find the limit:

\lim_{x \to 3} \sqrt{2x + 1} =

Find the limit:

\lim_{x \to 3} \sqrt{6x - 8} =

Find the limit:

\lim_{x \to -1} \sqrt{5 - 11x} =

Khan Academy Resources

Limits intro Limits and continuity: FAQ Using tables to approximate limit values Strategy in finding limits Estimating limit values from graphs Creating tables for approximating limits Infinite limits: algebraic Next steps after indeterminate form (finding limits)Limits at infinity of quotients with square roots Limits of trigonometric functions Estimating limits from tables Limits of combined functions: sums and differences Limits by direct substitution Strategy in finding limits Limits by factoring Infinite limits: graphical Limits of combined functions: products and quotients One-sided limits from graphs Conclusions from direct substitution (finding limits)Direct substitution with limits that don't exist Estimating limit values from graphs Limits of composite functions Limits intro Limits using trig identities Limits of piecewise functions Limits at infinity: graphical Connecting limits and graphical behavior One-sided limits from tables Limits at infinity of quotients Limits by factoring Limit properties Limits of piecewise functions: absolute value Limits at infinity of quotients (Part 1)Limits at infinity of quotients (Part 2)Limits at infinity of quotients with square roots (odd power)Limits intro Introduction to infinite limits One-sided limits from graphs Limits at infinity of quotients with square roots (even power)Infinite limits and asymptotes Limits of trigonometric functions Strategy in finding limits Connecting limits and graphical behavior Analyzing unbounded limits: rational function Introduction to limits at infinity Functions with same limit at infinity Trig limit using double angle identity Limit of sin(x)/x as x approaches 0 One-sided limits from tables Limits by rationalizing Limits of composite functions: external limit doesn't exist Analyzing unbounded limits: mixed function Limit of (1-cos(x))/x as x approaches 0 Limits of composite functions: internal limit doesn't exist Theorem for limits of composite functions: when conditions aren't met Approximating limits using tables Trig limit using Pythagorean identity Limits of combined functions: piecewise functions Estimating limits from tables Estimating limit values from graphs Limits of piecewise functions Limits by direct substitution One-sided limits from graphs: asymptote Undefined limits by direct substitution Theorem for limits of composite functions Unbounded limits Limits of combined functions

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