Posted by Rob on Friday, December 16, 2011 at 1:46am.
prove that 5x  7  sin3x = 0 has at least one zero and prove that it has exactly one real zero.
How am I supposed to show my work for this? I don't really understand how to show my work for the IVT. Without that I can't do any work for the MVT.

calculus  drwls, Friday, December 16, 2011 at 2:23am
Draw graphs of 5x  7 and sin3x and see how many times they intersect. They only cross once, at about x = 1.27. That can be clearly seen from the two graphs.
I believe in doing things the easy way. I don't see how either the mean or intermediate value theorems will be useful here, but math is not my specialty.
5x  7 only has values that are in the +/ 1 range of sin 3x when x is between 1.2 and 1.6. Perhaps that will help with a more formal proof.
You only have to consider the function
5x  7  sin3x between x = 1.2 and x = 1.6.
In that interval, it goes from 0.5575 to 1.996.
The slope remains positive so it can only equal zero once.
Answer This Question
Related Questions
 calculus  Prove that there is a number that is exactly one more than its cube...
 Calculus (Please Check)  Show that the equation x^5+x+1 = 0 has exactly one ...
 Calculus  Show that the function f(x)= x^(3) +3/(x^2) +2 has exactly one zero ...
 Maths Help  (1) Prove that the cancellation law of multiplication is equivalent...
 IB HL Math  I need to that if there is better way to prove the following: I am ...
 Calculus I  Show that the equation x^4 + 4x + c = 0 has at most two real roots...
 Discrete Math Help  1) How would I prove that (n  1 + 2 C 2) = n + (n C 2) 2) ...
 calculus  A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)...
 Math  ok so i'm kinda sort of confused... I had this for a equation X^2 + 4X  ...
 discrete math  1)prove that if x is rational and x not equal to 0, then 1/x is ...
More Related Questions