(a) find the differential dy. y = 3 tan(x) dy = 3 sec²(x)dx (b) evaluate dy for the given values of x and…

(a) find the differential dy. y = 3 tan(x) dy = 3 sec²(x)dx (b) evaluate dy for the given values of x and dx. x = π/4, dx = -0.1 dy = enter a number. need help? read it submit answer

(a) find the differential dy. y = 3 tan(x) dy = 3 sec²(x)dx (b) evaluate dy for the given values of x and dx. x = π/4, dx = -0.1 dy = enter a number. need help? read it submit answer

Answer

Explanation:

Step1: Recall the differential formula

We know from part (a) that $dy = 3\sec^{2}(x)dx$.

Step2: Substitute given values

Substitute $x=\frac{\pi}{4}$ and $dx = - 0.1$ into the formula. Since $\sec(x)=\frac{1}{\cos(x)}$ and $\cos(\frac{\pi}{4})=\frac{\sqrt{2}}{2}$, then $\sec(\frac{\pi}{4})=\sqrt{2}$. So $\sec^{2}(\frac{\pi}{4}) = 2$. Then $dy=3\times2\times(-0.1)$.

Step3: Calculate the result

$dy = 3\times2\times(-0.1)=-0.6$.

Answer:

$-0.6$