Problem to solve
Compute \[ \lim_{ x \to -\infty } [2x^3-12x^2+x-7] \]
Solution
STEP 1
Find the following limit: lim_(x->-∞)(2 x^3 - 12 x^2 + x - 7)
STEP 2
Hint: | The limit of a polynomial at -∞ is the limit of its highest order term. lim_(x->-∞)(2 x^3 - 12 x^2 + x - 7) = lim_(x->-∞) 2 x^3: lim_(x->-∞) 2 x^3
STEP 3
Hint: | If neither of the terms of a product approach 0 as x->a, then by the product rule, the limit of the product is the product of the limits. Applying the product rule, write lim_(x->-∞) 2 x^3 as 2 lim_(x->-∞) x^3: 2 lim_(x->-∞) x^3
STEP 4
Hint: | Apply the power rule. Using the power rule, write lim_(x->-∞) x^3 as (lim_(x->-∞) x)^3: 2 (lim_(x->-∞) x)^3
STEP 5
Hint: | As x approaches -∞, x approaches... lim_(x->-∞) x = -∞: 2 (-∞)^3
STEP 6
Hint: | Evaluate 2 ((-∞)^3). 2 ((-∞)^3) = -∞: Answer: | | -∞
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Edited by tododemate® - 2021