Questions in Section Calculus I

Compute the derivative of `5xe^x-4cos(x)`.

Find the equation of the tangent line to the curve `y=5x^2-3^x` at `(1,2)`.

Use the following graph to evaluate a) `f'(1)` and b) `f'(6)`:

Use the Maclaurin series of the function `1/(1-x)` to find the Maclaurin series of `x/(1-x)^2`.

Find `f(g(x))` if `f(x)=1/x` and `g(x)=(4-x)/(2+x)`

Find the equation of the tangent line to the graph `x^2+y^2-3xy=-11x` at the point `(-1,2)`.

  1. Find the differential `dy` for `y=6tan(x)`
  2. Evaluate `dy` for the given values of `x` and `dx`: `x=pi/3`, `dx=-0.1`

Let `f(x)=ax^2+bx+c`. Find `a`, `b`, `c` so that the tangent to the graph of `y=f(x)` at `(1,5)` has a slope of `1` and `f(0)=-5`.

Find the critical numbers of `f(x)=10x^2+6x`

Find `lim_(x->0)(ln(x))^tan(x)`.

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