Let $$f(x)= x^4+2$$ be a one-to-one function. If $$g(x)$$ is its inverse and $$f(2)=18$$, which of the following represents the correct value of $$g'(18)$$?

Which of the following is the correct derivative $$\frac{dy}{dx}$$ for the equation $$\sin(x)+\sin(y)=x*y$$ obtained through implicit differentiation?

Solve the equation: $$\lim_{x\to1}\frac{\sqrt{x+3}-2}{x-1}$$.

The function $$f$$ is defined by $$f(x) = \frac{x^2 - 4}{x^2 + 1}$$. On which of the following intervals is the graph of $$f$$ concave up?

Consider a function $$h$$ where $$\displaystyle \lim_{x \to 4^-} h(x) = 6$$, $$\displaystyle \lim_{x \to 4^+} h(x) = 6$$, and $$h(4)$$ is undefined. Which of the following statements is correct?

If $$y=\left(\frac{3x+2}{2x-3}\right)^4$$, then $$\frac{dy}{dx}=$$?

Consider a function $$s$$ defined on the interval $$(-3, 3)$$. If $$s$$ is continuous at $$x = 0$$ and $$\displaystyle\lim\limits_{x \to 0} \frac{s(x) - s(0)}{x}$$ exists and equals $$-5$$, which of the following can be concluded?

I. For the concentration function $$S(t)=200-15*t^2+t^3$$, differentiating gives $$S'(t)=-30*t+3*t^2$$. II. Evaluating at $$t=3$$ yields $$S'(3)=-30*3+3*9=-90+27=-63$$. III. The negative value of $$S'(3)$$ indicates that the concentration is decreasing at $$t=3$$. Which of the above statements are true regarding the rate of change of the solute concentration?

Which of the following is the solution to the differential equation $$\frac{dy}{dx}=y\cos(x)$$ whose graph contains the point (0, 3)?

A particle’s velocity is given by $$v(t)=3*t^2-4*t+2$$ and its acceleration by $$a(t)=6*t-4$$. Solve the equation $$6*t-4=8$$ to determine the time t (in seconds) at which the particle’s acceleration is $$8\,m/s^2$$.

A particle moves along the $$x$$-axis so that at any time $$t$$, $$t \geq 0$$, its acceleration is $$a(t) = 6\cos 3t$$. If the velocity of the particle at $t

At time $$ t = 0 $$, the population is 240 hundred fish and is increasing at the rate of 72 hundred fish per day. Which of the following is an expression for $$ P(t) $$?

Which of the following is an example of a right-hand Riemann sum approximation for the area under a curve, as represented by the table above?

The graph above shows f(x) = $$\sqrt{x}$$. Compute the average rate of change on the interval [4, 9] and the instantaneous rate of change at x = 9, then find the difference between these two values.

Let $$ K(x) $$ be an antiderivative of $$ \frac{5x^2 + \ln(x+1)}{x^2 + 9} $$. If $$ K(3) = -4 $$, then $$ K(1) = $$ ?

$$\displaystyle \lim_{x \to \infty} \frac{10 - 6x^2}{5 + 3e^x}$$ is

If $$\displaystyle f(x) = x^{\frac{5}{2}} - 7x^{-\frac{1}{2}}$$, then $$\displaystyle f'(4) =$$

The points $$(0, 0)$$ and $$(1, 1)$$ are on the graph of a function $$y = f(x)$$ that satisfies the differential equation $$\displaystyle \frac{dy}{dx} = y - x^2$$. Which of the following must be true?

If $$\displaystyle\int_0^4 f'(t) \, dt = 8$$, then $$f(4) = $$ ?

Using the table above, which of the following represents the trapezoidal sum approximation for the integral over the interval from $$t=2$$ to $$t=10$$?