Exercises for Question Type 1: Drawing graphs of specific functions to determine their limits at specific places

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Exercises for Question Type 1: Drawing graphs of specific functions to determine their limits at specific places - IB

Question 1

Use a table of values for x = - 1, - 2, - 4, - 10 to estimate x \to - \infty lim e^{x} .

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Question 2

This question assesses the ability to estimate one-sided limits using numerical approximation and a table of values.

Use a table of values for x = 2.1, 2.01, 2.001 to estimate the one-sided limit x \to 2^{+} lim \frac{1}{x - 2} .

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Question 3

Using the values x = 0.9, 0.99, 0.999, 1.1, 1.01, 1.001, estimate the value of x \to 1 lim \frac{1}{x} .

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Question 4

Estimate x \to 0 lim \frac{e ^{x} - 1}{x} using x = 0.1, 0.01, 0.001 .

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Question 5

The question asks for a numerical estimation of the limit of a sequence related to the definition of Euler's number e .

Use the sequence a_{n} = (1 + \frac{1}{n})^{n} for n = 10, 100, 1000 to estimate n \to \infty lim (1 + \frac{1}{n})^{n} .

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Question 6

Evaluate lim_{x \to \infty} \frac{1}{x} by examining x = 10, 100, 1000 .

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Question 7

Consider the behavior of the function f (x) = \frac{1}{x} as x approaches zero from the left.

Use a table of values for x = - 0.1, - 0.01, - 0.001 to estimate x \to 0^{-} lim \frac{1}{x} .

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Question 8

Use the values x = 2, 10, 100, 1000 to estimate the value of x \to \infty lim x^{1/ x} .

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Question 9

Estimating limits of exponential functions using a table of values.

Estimate x \to \infty lim e^{- x} using x = 1, 2, 4, 10 .

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Question 10

Estimate the limit of a function using a numerical approach by evaluating the function at points approaching the limit point from one side.

Estimate x \to 0^{+} lim \frac{1}{x ^{2}} using x = 0.1, 0.01, 0.001 .

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Question 11

Use a table of values for x = 0.1, 0.01, 0.001 to estimate x \to 0^{+} lim \frac{1}{x} .

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Question 12

Use a table of values for x = 1.9, 1.99, 1.999 to estimate the one-sided limit x \to 2^{-} lim \frac{1}{x - 2} .

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IB Mathematics Applications & Interpretation Question Type 1: Drawing Graphs of Specific Functions to Determine Their Limits at Specific Places Exercises