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lim 5x - 4 x→1 lim |7x + 10| x→-3 lim x²(x + 1) x→-2

Mathematics

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Answer

1\text{1}

11\text{11}

-4\text{-4}

Step-by-step solution

8 steps

Here are the solutions for the limits:

  • First Limit:

  1. Substitute x=1x=1 into the expression 5x−45x - 4.

    $$
\lim_{x \to 1} (5x - 4) = 5(1) - 4
$$

  2. Simplify the expression.

    $$
5 - 4 = 1
$$
The limit is $\boxed{\text{1}}$.
    • Second Limit:

  3. Substitute x=−3x=-3 into the expression ∣7x+10∣|7x + 10|.

    $$
\lim_{x \to -3} |7x + 10| = |7(-3) + 10|
$$

  4. Simplify the expression inside the absolute value.

    $$
|-21 + 10| = |-11|
$$

  5. Calculate the absolute value.

    $$
|-11| = 11
$$
The limit is $\boxed{\text{11}}$.
    • Third Limit:

  6. Substitute x=−2x=-2 into the expression x2(x+1)x^2(x + 1).

    $$
\lim_{x \to -2} x^2(x + 1) = (-2)^2(-2 + 1)
$$

  7. Simplify the terms.

    $$
(4)(-1)
$$

  8. Multiply the values.

    $$
4 \times -1 = -4
$$
The limit is $\boxed{\text{-4}}$.
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