Find the limit by creating a table of values. lim x → 0 − 4 x + 2 \lim_{x\rarr0}-4x+2 lim x → 0 − 4 x + 2

In this problem, we're asked to find the limit by creating a table of values, and the limit that we wanna find here is the limit of negative 4x+2 as x approaches 0. Now here, since we're trying to find the limit as x approaches 0, we want to look at values really, really close to 0. So by creating a table of values here, I'm going to put 0 in the middle because I want to look at values getting really, really close to 0 on this side but are actually less than 0. So values like negative 0.01 and negative 0.1. Now I wanna plug these values into my function, negative 4 x plus 2. So doing that for this first value of negative 0.1, I get negative 4 times negative 0.1 plus 2 which will give me a value of 2.04. Now if I do the same thing here for this negative 0.01, this will actually give me a value of 2.004. So we can already see here that these values seem to be approaching 2 for my function as x approaches 0. But we, of course, want to look at values that are actually greater than 0 but really, really close to it, again, approaching 0 from this other side. So So I wanna think of values like a 0.01 and a 0.1. Now plugging these values into my function here, if I plug in this 0.01, that's going to give me a value of 1.96. And if I do the same thing for 0.1, again, plugging that into my function and negative 4x+2, that will give me a value of 1.6. So we see coming in from this side that we are again approaching 2 the same way that we saw on that left side. So here, the limit of negative 4x plus 2 as x approaches 0 is going to be equal to 2. And that's our limit here. I'll see you in the next one.

1. Limits and Continuity

Introduction to Limits

Business Calculus

1. Limits and Continuity

Introduction to Limits

Struggling with Business Calculus?

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Multiple Choice

Find the limit by creating a table of values.
$\lim_{x\rarr0}-4x+2$

$-4$

$-2$

$0$

$2$

Verified step by step guidance

Step 1: Understand the problem. The goal is to find the limit of the function $-4x + 2$ as $x$ approaches 0. A table of values will help us observe the behavior of the function near $x = 0$.

Step 2: Choose values of $x$ that are close to 0 from both the left (negative side) and the right (positive side). For example, you might choose $x = -0.1, -0.01, 0, 0.01, 0.1$.

Step 3: Substitute each chosen value of $x$ into the function $-4x + 2$ to calculate the corresponding $y$-values. For example, if $x = -0.1$, then $y = -4(-0.1) + 2 = 0.4 + 2 = 2.4$. Repeat this for all chosen $x$-values.

Step 4: Record the $x$-values and their corresponding $y$-values in a table. Observe how the $y$-values behave as $x$ gets closer to 0 from both sides.

Step 5: Analyze the table. If the $y$-values approach a single number as $x$ approaches 0, that number is the limit. In this case, observe that the $y$-values approach 2 as $x$ approaches 0.