Evaluate the following limit. If the answer is positive infinite, type \"I\"; if

Question

Evaluate the following limit. If the answer is positive infinite, type "I"; if negative infinite, type "N"; and if it does not exist, type "D' lim x rightarrow infinity(square root x^2 + 6x - square root x^2 + 3x) Evaluate the following limit. If the answer is positive infinite, type "I"; if negative infinite, type "N"; and if it does not exist, type "D". lim x rightarrow infinity (square root 3x^2 + 8x + 6 - square root 3x^2 + 3x + 1) Which of the following functions satisfy the following conditions? Find the limits as (a) x rightarrow infinity and (b) rightarrow -infinity. Write "I" for infinity or "N" for negative infinity below. [Can you use this information, along with the intercepts, to give a rough sketch of the graph?] Find lim x rightarrow infinity f(x) if 4x - 1/x

Explanation / Answer

1) lim x -> infinity sqrt(x^2 +6x) - sqrt(x^2 +3x)

Multiplying and dividing by sqrt(x^2 +6x) + sqrt(x^2 +3x)

==> lim x -> infinity sqrt(x^2 +6x) - sqrt(x^2 +3x)    *   [sqrt(x^2 +6x) + sqrt(x^2 +3x)]/[sqrt(x^2 +6x) + sqrt(x^2 +3x)]

==> lim x -> infinity {(x^2 +6x) - (x^2 +3x) }/[sqrt(x^2 +6x) + sqrt(x^2 +3x)]

==> lim x -> infinity {3x }/[sqrt(x^2 +6x) + sqrt(x^2 +3x)]

==> Positive infinity : I

2) lim x -> infinity sqrt(3x^2 +8x +6) - sqrt(3x^2 +3x +1)

Multiplying and dividing by sqrt(3x^2 +8x +6) + sqrt(3x^2 +3x +1)

==> lim x -> infinity sqrt(3x^2 +8x +6) - sqrt(3x^2 +3x +1) * [sqrt(3x^2 +8x +6) + sqrt(3x^2 +3x +1)]/[sqrt(3x^2 +8x +6) + sqrt(3x^2 +3x +1)]

==> lim x -> infinity (3x^2 +8x +6) - (3x^2 +3x +1)/[sqrt(3x^2 +8x +6) + sqrt(3x^2 +3x +1)]

==> lim x -> infinity (5x -5) /[sqrt(3x^2 +8x +6) + sqrt(3x^2 +3x +1)]

==> positive infinity : I

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