Equation of Perpendicular Line to Tangent Line at f(x)= x√x P(1,1)

[Maliken]

Homework Statement

find the equation of the line perpendicular to the tangent line at the given point f(x)= x√x P(1,1)

Homework Equations

f(a+h) - f(a) / h

The Attempt at a Solution

ok so first i replace (f(a) and f(a+h) in the equation x√x, and then i get

1. a+h√a+h - a√a / h, then i rationalize the numerator and then i get
2. a+h)^2(a+h) - a^2(a) / h(a+h)√a+h + a√a

and if i try expanding this etc i just get indeterminate form.. where did i go wrong ?i still get indeterminate form even after using 1 instead of a

 

[Maliken]

oh and btw i haven't learned derivatives, so i have to use limits

 

[Mark44]

Homework Statement

find the equation of the line perpendicular to the tangent line at the given point f(x)= x√x P(1,1)

Homework Equations

f(a+h) - f(a) / h

Your formula needs more parentheses. What you wrote means
$$f(a + h) - \frac{f(a)}{h}$$
There need to be parentheses around the entire numerator, like so: (f(a+h) - f(a)) / h
To look really nice, you can use LaTeX (see https://www.physicsforums.com/threads/physics-forums-faq-and-howto.617567/#post-3977517)

The Attempt at a Solution

ok so first i replace (f(a) and f(a+h) in the equation x√x, and then i get

1. a+h√a+h - a√a / h, then i rationalize the numerator and then i get
2. a+h)^2(a+h) - a^2(a) / h(a+h)√a+h + a√a

Both the above are really hard to read, due to many missing parentheses. For one, the entire numerator needs parentheses around it. For another, a + h√a + h doesn't mean what you intend, which is that a + h is multiplying √(a + h). Also, in #2, you are missing a left parenthesis at the beginning of the line.

and if i try expanding this etc i just get indeterminate form.. where did i go wrong ?i still get indeterminate form even after using 1 instead of a

Please rewrite the two expressions above so that we can read them.

 

[Ray Vickson]

Homework Statement

find the equation of the line perpendicular to the tangent line at the given point f(x)= x√x P(1,1)

Homework Equations

f(a+h) - f(a) / h

The Attempt at a Solution

ok so first i replace (f(a) and f(a+h) in the equation x√x, and then i get

1. a+h√a+h - a√a / h, then i rationalize the numerator and then i get
2. a+h)^2(a+h) - a^2(a) / h(a+h)√a+h + a√a

and if i try expanding this etc i just get indeterminate form.. where did i go wrong ?i still get indeterminate form even after using 1 instead of a

You definitely do NOT want what you wrote, which was
f(a+h)- \frac{f(a)}{h}
Can you see how to write things properly?

 

[Maliken]

ok I am sorry lol i didnt know about latex , i got it though so thanks i guess

i forgot to expand one of my binomials

 

[Ray Vickson]

ok I am sorry lol i didnt know about latex , i got it though so thanks i guess

i forgot to expand one of my binomials

You do not need LaTeX; you need parentheses, like this: [f(a+h) - f(a)]/h. You need to make sure that when your expressions are read by standard parsing rules they come out saying what you want. Remember: multiplication and division have higher priority than addition and subtraction, etc.