For each curve, plug in the given point 
and check if the equality holds. For example:
(I) (2, 3) does lie on 
since 2^2 + 2*3 - 3^2 = 4 + 6 - 9 = 1.
For part (a), compute the derivative 
, and evaluate it for the given point . This is the slope of the tangent line at the point. For example:
(I) The derivative is
so the slope of the tangent at (2, 3) is
and its equation is then
For part (b), recall that normal lines are perpendicular to tangent lines, so their slopes are negative reciprocals of the slopes of the tangents, 
. For example:
(I) The tangent has slope 7/4, so the normal has slope -4/7. Then the normal line has equation
Answer:
Integral will be diverging in nature
Step-by-step explanation:
We have given integral 
Now after solving the integral
![[\frac{3}{2}\frac{x^3}{3}]](https://tex.z-dn.net/?f=%5B%5Cfrac%7B3%7D%7B2%7D%5Cfrac%7Bx%5E3%7D%7B3%7D%5D)
limit from 5 to infinite
So ![[\frac{3}{2}\frac{\infty^3}{3}]-[\frac{3}{2}\times \frac{5^3}{3}]=\infty](https://tex.z-dn.net/?f=%5B%5Cfrac%7B3%7D%7B2%7D%5Cfrac%7B%5Cinfty%5E3%7D%7B3%7D%5D-%5B%5Cfrac%7B3%7D%7B2%7D%5Ctimes%20%5Cfrac%7B5%5E3%7D%7B3%7D%5D%3D%5Cinfty)
As after solving integral we got infinite value so integral will be diverging in nature
Answer:
x = ± 2
Step-by-step explanation:
Given
f(x) = x² + 1 and (x, 5 ) is a solution then f(x) = 5
Equating the two gives
x² + 1 = 5 ( subtract 1 from both sides )
x² = 4 ( take the square root of both sides )
x = ± 
= ± 2
Thus (- 2, 5) and (2, 5) are solutions
<span>I rounded up the whole number as if each student sells only 3 sweatshirts, it is too little to pay for the whole trip, therefore the number must be 4. Hope that helps!</span>
