Answer to Question #87285 in Calculus for Joshua

Question

x2−5t−9
4.Evaluate the limit lim x → −∞ ---------
2x^4+3x^3
a.4
b.2
c.0
d.1

5.Given y(x)=x^4−4x^3+3x^2−5x, evaluate d^4y
-----
dx^4
a.30
b.42
c.24
d.22

Answer 1

$$4.\ \lim\limits_{x\rarr - \infin }{{x^2-5x-9} \over {2x^4+3x^3}}=\lim\limits_{x\rarr - \infin }{{x^2/x^4-5x/x^4-9/x^4} \over {2x^4/x^4+3x^3/x^4}}=$$

$$=\lim\limits_{x\rarr - \infin }{{1/x^2-5/x^3-9/x^4} \over {2+3/x}}={{0+0-0} \over {2-0}}=0$$

$$c. \ 0$$

$$5.\ {dy \over dx}=4x^3-12x^2+6x-5$$

$${d^2y \over dx^2}=12x^2-24x+6$$

$${d^3y \over dx^3}=24x-24$$

$${d^4y \over dx^4}=24$$

$$c. \ 24$$