Question

lim [sqrt(1+3x^4) - sqrt(1-2x) ] / (x+x^2+2x^3) . x->0

Answer 1

try rationalizing the numerator

Answer 2

\[\lim_{x \rightarrow 0}\frac{\sqrt{1+3x^4}-\sqrt{1-2x}}{x(1+x+2x^2)} \cdot \frac{\sqrt{1+3x^4}+\sqrt{1-2x}}{\sqrt{1+3x^4}+\sqrt{1-2x}}\]

Answer 3

\[\lim_{x \rightarrow 0}\frac{(1+3x^4)-(1-2x)}{x(1+x+2x^2)(\sqrt{1+3x^4}+\sqrt{1-2x})}\]

Answer 4

\[\lim_{x \rightarrow 0}\frac{3x^4+2x}{x(1+x+2x^2)(\sqrt{1+3x^4}+\sqrt{1-2x})}\]

Answer 5

now factor the top and cancel an x

Answer 6

\[\lim_{x \rightarrow 0}\frac{x(3x^3+2)}{x(1+x+2x^2)(\sqrt{1+3x^4}+\sqrt{1-2x})}\]

Answer 7

\[\lim_{x \rightarrow 0}\frac{3x^3+2}{(1+x+2x^2)(\sqrt{1+3x^4}+\sqrt{1-2x})}\]

Answer 8

what happens if you plug in 0 now?

Answer 9

I'll get my answer . Thank you so much!