calculus

posted by .

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 -

    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

First Name
School Subject
Your Answer

Similar Questions

  1. 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 non-prime, then: Let a = 6 Let r = 4 6! (6 – 4)! 4! = 3(2) x 5 x 4! …
  2. 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 …
  3. 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?
  4. Maths Help

    (1) Prove that the cancellation law of multiplication is equivalent in a commutative ring to the assertion that the product of non-zero factors is not zero. (2) For any given Integral Domain, state the law of Trichotomy, and show that …
  5. calculus

    A) How do you prove that if 0(<or=)x(<or=)10, then 0(<or=)sqrt(x+1)(<or=)10?
  6. 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)= cosx-x has a zero in (o. pi/2) Justify.
  7. 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.
  8. 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 …
  9. 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 …
  10. 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

More Similar Questions