Question

If sinhx=3 then find the value of cosh(3x). Also show that x =
$log_{e}(3 + \sqrt{10} )$
​

Answer 1

Answer:

Consider a function f that is differentiable at a point x=a. Recall that the tangent line to the graph of f at a is given by the equation

y=f(a)+f^{\prime}(a)(x-a).

For example, consider the function f(x)=\frac{1}{x} at a=2. Since f is differentiable at x=2 and f^{\prime}(x)=-\frac{1}{x^2}, we see that f^{\prime}(2)=-\frac{1}{4}. Therefore, the tangent line to the graph of f at a=2 is given by the equation

y=\frac{1}{2}-\frac{1}{4}(x-2).

Step-by-step explanation:

a graph of f(x)=\frac{1}{x} along with the tangent line to f at x=2. Note that for x near 2, the graph of the tangent line is close to the graph of f. As a result, we can use the equation of the tangent line to approximate f(x) for x near 2. For example, if x=2.1, the y value of the corresponding point on the tangent line is

y=\frac{1}{2}-\frac{1}{4}(2.1-2)=0.475.

The actual value of f(2.1) is given by

from 2, the equation of the tangent line does not give us a good approximation. For example, if x=10, the y-value of the corresponding point on the tangent line is

y=\frac{1}{2}-\frac{1}{4}(10-2)=\frac{1}{2}-2=-1.5,

whereas the value of the function at x=10 is f(10)=0.1