On a coordinate plane, a curve approaches x = negative 3, has inflection point (0, 1), and approaches x = 3 in quadrant 1 and 4. A curve approaches x = 3 in quadrant 1, and another curve approaches x = negative 3 in quadrant 3. Use the graph of f(x) to describe the limits of the function.

Limit of f (x) as x approaches 3 minus=
and Limit of f (x) as x approaches 3 plus=

Limit of f (x) as x approaches negative 3 minus=
and Limit of f (x) as x approaches negative 3 plus=

General Formulas and Concepts:

Algebra I

Algebra II

Calculus

Limits

Graphical Limits

Step-by-step explanation:

We approach this question by analyzing the graph. We notice we have asymptotes at x = -3 and x = 3.

Question 1

Essentially, the question is asking what the value is for f(x) when x approaches 3 from the left. We see from the graph f(x) that if we approach 3 from the left, we would be going towards the x = 3 asymptote, specifically -∞.

∴

Question 2

Essentially, the question is asking what the value is for f(x) when x approaches 3 from the right. We see from the graph f(x) that if we approach 3 from the right, we would be going towards the x = 3 asymptote, specifically ∞.

∴

Question 3

Essentially, the question is asking what the value is for f(x) when x approaches -3 from the left. We see from the graph f(x) that if we approach -3 from the left, we would be going towards the x = -3 asymptote, specifically -∞.

∴

Question 4

Essentially, the question is asking what the value is for f(x) when x approaches -3 from the right. We see from the graph f(x) that if we approach -3 from the right, we would be going towards the x = -3 asymptote, specifically ∞.

∴

Topic: AP Calculus AB/BC (Calculus I/II)

Unit: Limits

Book: College Calculus 10e

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

step-by-step explanation:

given   that triangle lno is congruent to triangle lnm.

we have to fill up the blanks in the given question.

according to above order of congruency   kept in mind we can say that

∠lno ≅ ∠lnm

∠oln ≅ ∠mln

ln ≅ ln due to common in both.

hence, by sas congruency,

the side angle side rule   states that if two sides and the included angle of one triangle are congruent to another triangle, then these two triangles are congruent.