# Using the Tangent Line to Approximate Function Values

When navigating the intricate terrain of calculus, the tangent line emerges as a powerful tool for approximating function values with precision. This method hinges on the concept of linearity, where the tangent line at a specific point on a curve closely mirrors the behavior of the function nearby. By exploiting this relationship, mathematicians can swiftly estimate function values at nearby points, facilitating efficient analysis and problem-solving in various mathematical contexts. This technique serves as a cornerstone in calculus, offering a practical approach to understand and work with complex functions in a simplified manner.

Questions

- How do you find the linearization of #y = sin^-1x# at #x=1/4#?
- How do you find the linearization of #f(x) = sqrt(x)# at x=49?
- How do you find the linearization of #f(x)=4x^3-5x-1# at a=2?
- How do you find the linearization of #f(x) = 2x³ + 4x² + 6# at a=3?
- How do you find the linearization at (-2,1) of #f(x,y) = x^2y^3 - 4sin(x+2y) #?
- Approximate the value of ^3 sqrt 27.3 using the tangent line of f(x)= ^3 sqrt x at point x= 27?
- How do you use the tangent line approximation to approximate the value of #ln(1.006)# ?
- How do you find the linearization of #f(x)=cosx# at x=5pi/2?
- What is the local linearization of #y = (7+5x^2)^(-1/2)# at a=0?
- How do you find the linearization at x=0 of # f ' (x) = cos (x^2)#?
- How do you find the linearization at a=0 of #f(x)=1/1/(sqrt(2+x))#?
- How do you find the linearization at a=pi/6 of #f(x)=sinx#?
- How do you find the linearization at x=1 of #y = 2/x#?
- How do you find the linearization at (3,5,1) of # f(x,y,z) = sqrt(x^2 y^2 z^2)#?
- How do you find the linearization at a=1 of #f(x)=x^(3/4)#?
- How do you find the linear approximation #f(x)=2/x#, #x_0=1#?
- How do you find the linearization at (2,9) of #f(x,y) = xsqrty#?
- How do you find the linearization of #f(x)=x^3# at the point x=2?
- How do you find the linear approximation of a function?
- Let f(x) = 1/x and find the equation of the tangent line to f(x) at a "nice" point near 0.203, how do you use this to approximate 1/0.203?