How would you show the equation f(x) = 2x – 10 sin x – 2 has a root between 2 and 3 (where x is measured in radians)
With these kind of problems you are looking to find 2 values with which the output of the function is positive for one and negative for the other. In this scenario they have given 2 values 2 and 3 so the first step would be to input those to the equation.f(2) = -7.092974268... f(3) = 4.588799919...Since there is a sign change between the 2 values and f is a continuous function,there is therefore a root between the values between 2 and 3. It is vital when answering an exam question on this to give this reason as to why there is a root there otherwise you will normally not receive full marks.
KN
Answered by Kelvin N. • Further Mathematics tutor
3611 Views
See similar Further Mathematics A Level tutorsRelated Further Mathematics A Level answers
All answers ▸Expand (1+x)^3. Express (1+i)^3 in the form a+bi. Hence, or otherwise, verify that x = 1+i satisfies the equation: x^3+2*x-4i = 0.
Find the complex number z such that 5iz+3z* +16 = 8i. Give your answer in the form a + bi, where a and b are real numbers.
Find the Taylor Series expansion of tan(x) about π/4 up to the term in terms of (x-π/4)^3.
Prove by mathematical induction that 2^(2n-1) + 3^(2n-1) is divisible by 5 for all natural numbers n.