Question

can someone help me with this question? find the limit as x approaches 0 of (sqrt(1+x^2)-sqrt(1+x))/(sqrt(1+x^3)-sqrt(1+x))

Answer 1

http://arachnoid.com/latex/?equ=%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Csqrt%7B1%2Bx%5E2%7D-%5Csqrt%7B1%2Bx%7D%7D%7B%5Csqrt%7B1%2Bx%5E3%7D-%5Csqrt%7B1%2Bx%7D%7D%3D%20%5Clim_%7B%20x%20%5Cto%200%7D%20%5Cfrac%7B%5Csqrt%7B1%2Bx%5E2%7D-%5Csqrt%7B1%2Bx%7D%7D%7B%5Csqrt%7B1%2Bx%5E3%7D-%5Csqrt%7B1%2Bx%7D%7D%20%5Ccdot%20%5Cfrac%7B%5Csqrt%7B1%2Bx%5E3%7D%2B%5Csqrt%7B1%2Bx%7D%7D%7B%5Csqrt%7B1%2Bx%5E3%7D%2B%5Csqrt%7B1%2Bx%7D%7D%3D%20%5Clim_%7Bx%20%5Cto%200%7D%20%5Cfrac%7B%5Csqrt%7B1%2Bx%5E3%2Bx%5E2%2Bx%5E5%7D-%5Csqrt%7B1%2Bx%5E3%2Bx%2Bx%5E4%7D%2B%5Csqrt%7B1%2Bx%5E3%2Bx%5E2%2Bx%7D-1-x%7D%7Bx%5E3-x%7D%0A%20%20%5C%5C%20%5C%5C%20%5Ctext%7Bit%20is%20now%20in%20a%20good%20form%20to%20use%20Bernoulli%20de%20l'Hopital%2C%20because%20you%20can%20see%20that%20one%20differentiation%20is%20sufficient%20now%7D%20%5C%5C%20%5Ctext%7Bin%20fact%2C%20if%20you%20know%20about%20the%20mechanism%20of%20BdH%2C%20you%20can%20easily%20see%20that%20this%20converges%20to%201%2C%20because%20only%7D%20%5C%5C%20%5Ctext%7Bthe%202nd%2C%20the%203rd%20and%20the%20%24-x%24%20term%20survive%20the%20differentiation%20in%20the%20numerator.%7D

Answer 2

Sorry for the long link, but I didn't find another online source to typeset and link LaTeX and I am having doubts that LaTeX will come back to this website within the next couple of days/weeks