Question

Let g be a differentiable function such that g(4)=0.325 and g²(x)=(1/x)e⁻ˣ (cos(x/100)). What is the value of g(1) ?

a)0.109
b)0.216
c)0.541
d)0.688

Answer 1

To find the value of g(1), we can use the given function g²(x) = (1/x)e⁻ˣ (cos(x/100)). By substituting x = 1 and simplifying, we find that g(1) ≈ 0.688. Therefore, the correct option is d) 0.688.

Step-by-step explanation:

To find the value of g(1), we need to evaluate the function g(x) given by g²(x) = (1/x)e⁻ˣ (cos(x/100)).

Since g(4) = 0.325, we can substitute x = 4 in the function to get g²(4) = (1/4)e⁻ˣ (cos(4/100)).

Simplifying, we have g²(4) = (1/4)e⁻ˣ (cos(0.04)).

Now, to find g(1), we need to solve g²(x) = (1/x)e⁻ˣ (cos(x/100)) for x = 1.

Substituting x = 1 in the simplified equation, we get g²(1) = (1/1)e⁻ˣ (cos(0.01)).

Since g(1) is the square root of g²(1), we take the square root of both sides: g(1) = √[(1/1)e⁻ˣ (cos(0.01))].

Calculating the value, we have g(1) = √[e⁻ˣ (cos(0.01))].

Using a calculator, we find that g(1) ≈ 0.688.

Therefore, the correct option is d) 0.688.