Find the limit. lim x → 0 x 3 + 5 x 2 − 7 x + 3 \lim_{x\rarr0}x^3+5x^2-7x+3 lim x → 0 x 3 + 5 x 2 − 7 x + 3

In this problem, we're asked to find the limit of x cubed plus 5x squared minus 7x plus 3 as x approaches 0. So here we can just go ahead and plug 0 into this polynomial in order to get the limit. So this gives me a 0 cubed plus 5 times 0 squared minus 7 times 0 plus 3. Now all of these are going to end up being 0 so they all go away. And I am just left here with 3 as the limit of this function as x approaches 0. Let me know if you have any questions. I'll see you in the next one.

22. Limits & Continuity

Finding Limits Algebraically

Precalculus

NEW 22. Limits & Continuity

Finding Limits Algebraically

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Multiple Choice

Find the limit.
$\lim_{x\rarr0}x^3+5x^2-7x+3$

$0$

$2$

$3$

$5$

Verified step by step guidance

Identify the type of limit problem: This is a polynomial function, which is continuous everywhere. Therefore, the limit as x approaches any value is simply the value of the function at that point.

Substitute the value x = 0 into the polynomial function. The function given is $ x^3 + 5x^2 - 7x + 3 $.

Calculate each term of the polynomial separately: $ x^3 $ becomes $ 0^3 $, $ 5x^2 $ becomes $ 5(0)^2 $, $ -7x $ becomes $ -7(0) $, and the constant term is 3.

Add the results of each term: $ 0 + 0 + 0 + 3 $.

Conclude that the limit of the function as x approaches 0 is the sum of these values.