Example 3 Video Example < Find equations of the tangent line and normal line to the curve y=x√x at the point (9, 27). Illustrate by graphing the curve and these lines. Solution The derivative of f(x) = x√√x = xx¹²/² = x³/2 is f'(x) = So the slope of the tangent line at (9, 27) is f'(9) = ])(x-¯) y- y = y = The normal line is perpendicular to the tangent line, so its slope is the negative reciprocal of or 30 or We graph the curve and its tangent line and normal line in the figure below. 20 10 normal tangent Therefore an equation of the tangent line is 5 10 X 15 e , that is, .Thus the equation of the normal line is

Q: 10

A: To simplify 35+710.

Q: b. N(0)

A: Given,  r→t=sint, t, cost                   ...1

Q: 5.1 #7

A: Given that                  A=60-1054-403-3502-425, λ=5

Q: 12 X-

A: The solution is given below

Q: 31/2 / 1/2

A:

Q: 1 1 dx 3 5 x +x4

A:

Q: T. 9

A: Given: To determine: ST→ &amp; tan∠S

Q: 1. 2. 3.

A:

Q: 2 3 B={ A= 3 Find: A+B .B+A .A-

A:

Q: 1.6+0.4(x+6)+3.2

A: To simplify the expression means writing it in the simplest form.

Q: 619 d. 4 10

A:

Q: 9/12+3/24

A:

Q: (4 – a2)

A: To integrate.

Q: ne distance between the points on the gi

A:

Q: 198-33

A: Given: 198-33

Q: d 6

A: 5. In the given right triangle , the hypotenuse is 41 and the perpendicular length is 40. Apply the…

Q: expansion of (1-2m)“

A:

Q: 3. 18

A:

Q: 3. 2-1 da

A: Use the product rule to determine the derivative for the given…

Q: 12 8. 4

A: Given, 12/4 - 8/5 Taking LCM we have, LCM= 4*5= 20

Q: 人 2. 2. 4

A: The given integral is ∫x24-x2dx. Let x=2 sin u. Then dx=2 cosu du. Apply the substitution and…

Q: 12 10 6. X%=

A:

Q: Find A.

A: Given

Q: The columns of Q were obtained by applying the Gram-Schmidt process to the columns of A. Find an…

A: Solution by using Gram-Schmidt process as follows :

Q: 1. 12

A: We can use the concept of Pythagoras theorem to solve the given problem.