Can anyone help me to use a derivative of the definition of limit?
I do my homework and I am a problem. I do not want to use my real problem of the book, so I try to create a similar. I have only to see how they done that will help me a lot. Definition limits lim h-> 0 (f (x + h)-f (X)) / hf (x) = 8 – (x + 5) ^ 0.5 I know that the derivative f '(x) = -. 5 / (x + 5) ^ 0.5 When you use the definition of the limits to be I'm still fairly constant under the radical, since it can not get rid of it. Thanks
In fact, the exponent is correct – 0.5 f (x + h) = 8 – SQR (X + h + 5) f (x + h) – F (x) = 8 – SQR (x + 5 h) – [8 - SQR (x + 5)] ——–> SQR ( x + 5) – SQR (x + h + 5) is now divided by SQR [h (x + 5) - SQR (x + h + 5)] / h Now the trick …. mult number called by SQR (x + 5) + sqrt (x + h + 5) we obtain the simplification: [(x + 5) - (X + h + 5)] / {* H (SQR (X + 5) + sqrt (x + h + 5)) O} / {h * (sqrt (x + 5) + sqrt (x + h + 5 ))}, and H, will be canceled .. …… if, finally, lim h -> 0, -1 / {1 * (sqrt (x + 5) + sqrt (x + h + 5))} = – 1 / {2sqr (x + 5)}, or -0.5 (X + 5) ^ -0, 5
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