# Paisley Johnson

Calculus teacher | Tutor for 7 years

Greetings! I'm a passionate educator specializing in Calculus. I earned my degree from the University of South Dakota, where I delved deep into the intricacies of mathematical theory. With a commitment to fostering understanding and a knack for simplifying complex concepts, I'm here to guide you through the world of Calculus. Let's unravel the beauty of mathematics together and make learning an enriching experience!

## Questions

How do you find points of inflection for #y= sin x + cos x#?

What is the general solution for #dy/dx = 2y-3# ?

How do you implicitly differentiate #2=(x+2y)^2-xy-e^(3x+y^2) #?

What is the derivative of #arctan(x - sqrt(1+x^2))#?

How do you differentiate #y=(x^5+1)(3x^2-x)#?

What is #f(x) = int 1/(x-4) # if #f(2)=1 #?

What is the second derivative of # (x^2-1)^3#?

How do you find the derivative of #cos (2x)#?

How do you integrate #intx(4x+5)^3# using substitution?

How do you find the indefinite integral of ∫ (x - sinx ) dx / x^2 + 2 cosx ?

The region under the curves #x, y>=0, y=x^2sqrt(1-x^4)# is rotated about a) the x axis and b) the y axis. How do you sketch the region and find the volumes of the two solids of revolution?

A particle's acceleration along a straight line is given by #a(t)=48t^2+2t+6# . It's initial velocity is equal to -3cm/s and its initial position is 1 cm. Find its position function s(t). Answer is #s(t)=4t^4+1/3t^3+3t^2-3t+1# but I can't it figure out?

How do you implicitly differentiate #-1=(x+y)^2-xy-e^(3x+7y) #?

What is #lim t->-∞# of #(t^2+2)/(t^3+t^2-1)#?

What is #lim_ (xrarr0) (1/x -1/x^2-x)#?

What is the average value of the function # f(x) = 4x ln (2x) # on the interval #[1,4]#?

How do you integrate #int sqrt(1+2x)# using substitution?

Evaluate the integral of (x√x-3dx)?

If limit of #f(x)=27# as #x->c#, what the limit of #(f(x))^(3/2)# as #x->c#?

How do you differentiate #f(x)=(4e^x+1)(x-3)# using the product rule?