Find the equation of the line tangent to the graph at y=e^x at x =a

2 answers:

6 0

Answer: Find the first derivative of f(x). 2) Plug x value of the indicated point into f '(x) to find the slope at x. 3) Plug x value into f(x) to find the y coordinate of the tangent point. 4) Combine the slope from step 2 and point from step 3 using the point-slope formula to find the equation for the tangent line

Step-by-step explanation:

kaheart [24]3 years ago

3 0

Answer:

find derivative of function

sub in x value of point to find gradient of tangent

put gradient into y=(gradient)x+c

Sub in point and solve for c

you have found the equation of the tangent.

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The surface are I cannot find

Ilia_Sergeevich [38]

check the picture below.

so the triangular prism is really just 3 rectangles and 2 right-triangles,

now, we know the base of one of the triangles is 2.6, what's its height?

since it's a right-triangle, we can simply use the pythagorean theorem to get "h".

$\bf \textit{using the pythagorean theorem}
\\\\
c^2=a^2+b^2\implies \sqrt{c^2-a^2}=b
\qquad
\begin{cases}
c=\stackrel{hypotenuse}{5.2}\\
a=\stackrel{adjacent}{2.6}\\
b=\stackrel{opposite}{h}\\
\end{cases}
\\\\\\
\sqrt{5.2^2-2.6^2}=h\implies 4.5\approx h$

so, we can now, simply get the area of both of the triangles and the three rectangles and sum them up, and that's the area of the triangular prism.

$\bf \stackrel{two~triangles}{2\left[ \cfrac{1}{2}(2.6)(4.5) \right]}~~+~~\stackrel{rectangle}{(2.6\cdot 4.3)}~~+~~\stackrel{rectangle}{(4.3\cdot 3.9)}~~+~~\stackrel{rectangle}{(4.3\cdot 5.2)}
\\\\\\
11.7+11.18+22.36\implies \blacktriangleright 45.24 \blacktriangleleft$