Q:
# What is a tangent line approximation?

Tangent line approximation is used in calculus to approximate the values of a function based on its tangent. Tangent line approximation can be used because any curve examined closely at a particular point begins to bear similarities to a straight line, represented by the tangent.

Continue Reading
Credit:
LdF
E+
Getty Images

For example, for the function f(x) with a point x0, tangent line approximation can be used to approximate f near x0 by a simple linear function. The tangent line approximation f(x) is approximately equal to f(x0) + f'(x0)(x - x0). The last term on the right is the equation of a straight line in x. At x = x0, the term agrees with f(x), as it takes the value f(x0) and has the same slope as the tangent to the curve at x0.

Learn more about Trigonometry-
Q:
## How do you solve trigonometry problems?

A: Successfully working through trigonometry problems requires knowledge of the properties of triangles as well as the ability to measure and understand the r... Full Answer >Filed Under: -
Q:
## How do you find the cosine of pi?

A: The trigonometric functions sine, cosine and tangent calculate the ratio of two sides in a right triangle when given an angle in that triangle. To find the... Full Answer >Filed Under: -
Q:
## What is the derivative of tan (x)?

A: The derivative of the tangent of x is the secant squared of x. This is proven using the derivative of sine, the derivative of cosine and the quotient rule.... Full Answer >Filed Under: -
Q:
## What is the integral of secx?

A: The integral of sec(x) is the natural log of the absolute value of the secant of x plus the tangent of x, added to a constant. Using mathematical notation,... Full Answer >Filed Under: