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.

1. Limits and Continuity

Finding Limits Algebraically

Calculus

1. Limits and 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 function for which you need to find the limit: $ f(x) = x^3 + 5x^2 - 7x + 3 $.

Recognize that this is a polynomial function. Polynomial functions are continuous everywhere, which means you can find the limit by direct substitution.

Substitute $ x = 0 $ into the function: $ f(0) = 0^3 + 5(0)^2 - 7(0) + 3 $.

Simplify the expression: $ f(0) = 0 + 0 - 0 + 3 $.

Conclude that the limit of the function as $ x $ approaches 0 is the constant term, which is 3.