1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Ahat [919]
3 years ago
9

To find the equation of a line, we need the slope of the line and a point on the line. Since we are requested to find the equati

on of the tangent line at the point (4, 2), we know that (4, 2) is a point on the line. So we just need to find its slope. The slope of a tangent line to f(x) at x = a can be found using the formula
Mathematics
1 answer:
murzikaleks [220]3 years ago
8 0

Answer:

x-4y+4=0

f(x)=\sqrt x and x=4

Step-by-step explanation:

We are given that a curve

y=\sqrt x

We have to find the equation of tangent at point (4,2) on the given curve.

Let y=f(x)

Differentiate w.r.t x

f'(x)=\frac{dy}{dx}=\frac{1}{2\sqrt x}

By using the formula \frac{d(\sqrt x)}{dx}=\frac{1}{2\sqrt x}

Substitute x=4

Slope of tangent

m=f'(x)=\frac{1}{2\sqrt 4}=\frac{1}{2\times 2}=\frac{1}{4}

In given question

m=\lim_{x\rightarrow a}\frac{f(x)-f(a)}{x-a}

\frac{1}{4}=\lim_{x\rightarrow 4}\frac{f(x)-f(4)}{x-4}

By comparing we get a=4

Point-slope form

y-y_1=m(x-x_1)

Using the formula

The equation of tangent at point (4,2)

y-2=\frac{1}{4}(x-4)

4y-8=x-4

x-4y-4+8=0

x-4y+4=0

You might be interested in
A radio station is having a T-shirt design contest. The first prize is four times the second prize. The second price is four tim
hammer [34]
Answer:
The first prize is $800.

Explanation:
Third price = $50
The second price = $50(4) = $200
The first prize = 4($200) = $800
6 0
3 years ago
What is 0.2 in the 2 <br> keep going as a fraction
ollegr [7]
It is 2/10 for tour question
8 0
3 years ago
What is the equation of the linear function represented by the table?
3241004551 [841]

Answer:

gggggggggg

Step-by-step explanation:

gggggggggggg

8 0
3 years ago
Read 2 more answers
What is the graph of the equation 9x^2 + 4y^2 - 18x + 8y - 23 = 0 ?<br> Also, how did you get that?
Dmitriy789 [7]
13xy^2-10xy-23=0

you first add the like terms and rewrite and thats how you get the answer
8 0
3 years ago
Solve the following system of equations by using the inverse of a matrix.
Zepler [3.9K]

Answer:

(x, y, z) = (-8,4,-2)

Step-by-step explanation:

.......................................

6 0
3 years ago
Other questions:
  • the moon is 240,000 from earth what is the distance written as a whole number multiplied by a power of ten
    12·1 answer
  • A basketball player made 40% of the shots she attempted.if she made 32 baskets, how many shots did she attend?
    7·1 answer
  • alicia rides her bike 4 miles due north and 3 miles due west to a playground. What is the shortest distance to alicias home from
    7·1 answer
  • Form a polynomial f(x) with real coefficients having the given degree and zeros.
    15·1 answer
  • If a rectangle measures 1 1/2 by 4 find the area
    15·2 answers
  • Five thousand eight hundred nine-two people are going to a wedding. They can fit 80 people comfortably in each bus. How many bus
    7·2 answers
  • The perimeter of a rectangle is 40 inches. If the length of the rectangle is 13 inches, which equation could be used to find the
    9·1 answer
  • 18000 divided by 67= ?
    6·2 answers
  • Help with the top one ?
    10·1 answer
  • An arts academy requires there to be 6 teachers for every 108 students and 3 tutors for every 36 students. students How many stu
    11·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!