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Evaluate the following limits: (a) lim(5x+1) as x->2, (b) lim(2x²+6x-2) as x->1, (c) lim((x²-1)/(x-1)) as x->1, (d) lim(6x-2) as x->1, (e) lim(2x²+x) as x->-2

Mathematics

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Answers

2 parts
d
10
e
6

Step-by-step solution

7 steps

Here are the solutions to the limit problems:

Part d· 3 steps

Evaluate lim⁡x→2(6x−2)\lim_{x \to 2} (6x-2)

  1. Substitute the value x=2x=2 into the function.

    Since 6x−26x-2 is a polynomial function, we can find the limit by direct substitution.

    6(2)−26(2) - 2
  2. Perform the multiplication.

    12−212 - 2
  3. Perform the subtraction.

    1010

    The limit is 10\boxed{10}.

Part e6

Evaluate lim⁡x→−2(2x2+x)\lim_{x \to -2} (2x^2+x)

  1. Substitute the value x=−2x=-2 into the function.

    Since 2x2+x2x^2+x is a polynomial function, we can find the limit by direct substitution.

    2(−2)2+(−2)2(-2)^2 + (-2)
  2. Evaluate the exponent.

    2(4)+(−2)2(4) + (-2)
  3. Perform the multiplication.

    8−28 - 2
  4. Perform the subtraction.

    66

    The limit is 6\boxed{6}.

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