Limits + Continuity
The limit of 3x2-2x+1 as x→5.
What is 66?
The derivative of f(x)=4x
What is 4?
The approximate value of e.1 using a tangent line to f(x)=ex
What is 1.1?
The derivative of xy=1+x-y
What is y'=(1-y)/(1+x)?
The derivative of y=xx
What is (1+ln|x|)xx?
The type of discontinuity present in f(x)=x2/x
What is a removable discontinuity?
The derivative of f(x)=2x
What is 2xln2?
The approximate value of ln(1.5), using a tangent line to f(x)=ln(x)
What is .5?
The derivative of xy1/2=3
What is y'=-2y/x?
The derivative of y=sin(x)x
What is sin(x)x(xcot(x)+ln|sin(x)|)?
The limit as x→3 of f(x)=(x2-9)/(x-3)
What is 6?
The derivative of f(x)=(2+sin(x))5
What is 5(2+sin(x))4cos(x)?
The approximate value of sqrt(123) using an appropriate tangent line to f(x)=sqrt(x)
What is 11+1/11?
The derivative of sin(xy2)=x
What is y'=(1/cos(xy2)-y2)/2xy?
The derivative of y=(ln |x|)x
What is (ln |x|)x(ln|ln|x||+1/ln|x|)?
The limit as x→0 of f(x)=sin(x)/x
What is 1?
The derivative of f(x)=arccot(1+2x) (in reduced form)
What is -1/(1+2x+2x2)?
The approximate value of arctan(.04) using a tangent line to f(x)=arctan(x)
What is .04?
The derivative of arctan(x+y)=x
What is y'=(x+y)2?
The derivative of y=(x2+1)cot(x)
What is (x2+1)cot(x)(-csc2(x)ln(x2+1)+2xcot(x)/(x2+1))
The limit as x→0 of f(x)=(e3x-1)/(ex-1)
What is 3?
The derivative of f(x)=arcsec(e3x)
What is 3/(e6x-1)½?
The approximate value of sin(π/6+1/(4sqrt(3))) using an appropriate tangent line to f(x)=sin(x)
What is ⅝?
The derivative of sec(xy)=y+x
What is y'=(1-ysec(xy)tan(xy))/(xsec(xy)tan(xy)-1)?
The derivative of y=(arcsec(x))x+3
What is (arcsec(x))x+3(ln|arcsec(x)|+(x+3)/(|x|(x2-1)½arcsec(x)))?