What is the derivative of y = 3x2 ?
y' = 6x
Find the derivative of y = 3x2 ln(x)
y'=3x+ 6x ln(x)
Derivative of y=csc (x) at x=pi/4
-sqrt(2)/4
What is the coefficient of (x-2)3 in the Taylor series of lnx centered at x=2?
1/4
Suppose a function f is approximated with a fourth-degree Taylor polynomial about x=1. If the maximum value of the fifth derivative between x=1 and x=3 is 0.01. Then the maximum error incurred using this approximation is... (give 5 decimals)
0.00267
Find the derivative of f(x) = 5
0
f(x) = (3x - 2x2)(5 + 4x)
f'(x)=-24x2 + 4x + 15
Let f be a function such that (f(2+h)-f(2))/h=5. Which of the following must be true? Choose all that apply.
I. f is continuous at x=2
II. f is differentiable at x=2
III. The derivative of f is continuous at x=2
I, II, and III
Find a second degree Maclaurin polynomial for h(x)=7xex
y=7x+7x2
How accurate would a fourth-degree Taylor polynomial for cos x about x=0 be to approximate the value of cos(0.8)? State the maximum error to 3 decimal places.
0.003
Find the derivative of f(x) = 6x3 + x - 2
f'(x)=18x2+ 1
Find the derivative of y = (5x - 2)/(x2 + 1)
y'=(-5x2 + 4x + 5)/(x2 + 1)2
limh->0(e-1-h-e-1)/h=
-1/e
Suppose that g is a function such that g(5)=3, g'(5)=-2, g''(5)=7, and g'''(5)=-3.
Write a third degree Taylor Polynomial centered at x=5 and use this to approximate g(4.9).
3.236
Freebie! Pick a number 1-10. If you get the correct number, you get the 300 points for this question
2
Find the derivative of f(x) = 3sinx - 2cosx
f'(x)=3cosx + 2sinx
Find the derivative of f(x) = (2x + 5)/(x)1/2
f'(x)=(2x - 5)/(2x3/2)
Solve a and b in order for g(x) to be continuous and differentiable at x=0. What is a+b?
< ax+b when x>0
g(x)= <
< 1-x+x2 when x<=0
0
The Maclaurin series for f(x) is f(x)=1+x/2+(x^2)/6+(x^3)/24+....
f''(0)=?
1/3
Write a Maclaurin polynomial for function f that has derivatives of all orders on the interval (-1,1). Assume f(0)=1, f'(0)=-1/4, f''(0)=3/8, and the |f(4)(x)|<=6 for all x in the interval (-1,1). What is the maximum possible error for the approximation of f(0.5)?
(Round to 3 decimal places)
0.016
What is the equation of the tangent line to 13x4 + 3x2 - 6x +3 at x=1?
y-52=13(x-1) or y=13x+39
f(x)=x²sinx, what is f′(x)?
2xsinx+ x²cosx
f(x)=2g(x)+g(x)/h(x)
g(2)=3 g'(2)=-2
h(2)=-1 h'(2)=4
Find the equation of the tangent line in slope intercept form when x=2.
y=10x-17
x f(x) f'(x) f''(x) g(x) g'(x)
3 1 -2 7 4 -5
For n>=2, the nth derivative of g at x=3 is given by f(n)(3)=f(n-2)(3). Find the third degree Taylor polynomial for g(x) about x=3.
4-5(x-3)+(x-3)2/2-(x-3)3/3
The Taylor series about x=3 for a certain function f converges to f(x) for all x in the interval of convergence. The nth derivative of f at x=3 is given by
f(n)=(-1)n*n!/(5n(n+3)) and f(3)=1/3
What is the least degree polynomial needed to approximate f(4) with an error less than 1/4000.
Third degree