calculus
posted by Rob .
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
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.
Respond to this Question
Similar Questions

IB HL Math
I need to that if there is better way to prove the following: I am trying to prove that x r = k and k is a multiple of x only when x is prime. I said that if x is nonprime, then: Let a = 6 Let r = 4 6! (6 – 4)! 4! = 3(2) x 5 x 4! … 
Calculus
Show that the function f(x)= x^(3) +3/(x^2) +2 has exactly one zero on the interval (infinity, 0). So far this is what I have: 0=x^3 + 3/(x^2) +2 2= (1/x^2)(x^5 + 3) 2x^2= x^5 +3 But now I'm stuck. I also am not sure if this is … 
Math
ok so i'm kinda sort of confused... I had this for a equation X^2 + 4X  1 = 0 and then I was like zero? 
Maths Help
(1) Prove that the cancellation law of multiplication is equivalent in a commutative ring to the assertion that the product of nonzero factors is not zero. (2) For any given Integral Domain, state the law of Trichotomy, and show that … 
calculus
A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)sqrt(x+1)(<or=)10? 
calculus
Prove that there is a number that is exactly one more than its cube. (don’t solve just show there is one) Prove that the function f(x)= cosxx has a zero in (o. pi/2) Justify. 
Calculus I
Show that the equation x^4 + 4x + c = 0 has at most two real roots. I believe we're supposed to prove this by proof of contradiction using Rolle's Theorem, but I'm not quite sure how to do this problem. 
Calculus (Please Check)
Show that the equation x^5+x+1 = 0 has exactly one real root. Name the theorems you use to prove it. I.V.T. *f(x) is continuous *Lim x> inf x^5+x+1 = inf >0 *Lim x> inf x^5+x+1 = inf <0 Rolles *f(c)=f(d)=0 *f(x) is … 
Discrete Math Help
1) How would I prove that (n  1 + 2 C 2) = n + (n C 2) 2) A cafeteria offers 17 types of pizza and 5 types of soda. Bob goes there everyday for lunch, always buying two slices of pizza and one soda. However, he never gets exactly … 
Mathematics
mathematically, how to prove we cant divide by zero. and why multiplication of zero with any number leads to zero itself . can we mathematically prove that