Application of ...

Identify the false statement:

The percentage error in the $$11^{th}$$ root of the number $$28$$ is approximately ____________ times the percentage error in $$28$$

The slope of the normal to the curve $$y = 3x^2$$ at the point whose $$x$$-coordinate $$2$$ is

The slope of the tangent to the curve $$y=3{ x }^{ 2 }+3\sin { x } $$ at $$x=0$$ is

Consider the following statements:
$$1. y = \dfrac {e^{x} + e^{-x}}{2}$$ is an increasing function on $$[0, \infty)$$.
$$2. y = \dfrac {e^{x} - e^{-x}}{2}$$ is an increasing function on $$(-\infty, \infty)$$.
Which of the above statements is/are correct?

What is the slope of the tangent to the curve $$ x = t^2 + 3t - 8, y = 2t^2 - 2t - 5$$ at t = 2 ?

If the tangent to the function $$y = f(x)$$ at $$(3, 4)$$ makes an angle of $$\dfrac {3\pi}{4}$$ with the positive direction of x-axis in anticlockwise direction then $$f'(3)$$ is

How many tangents are parallel to x-axis for the curve $$ y = x^2 - 4x + 3$$ ?

The slope of the tangent to the curve given by $$x = 1 - \cos { \theta  }$$, $$y = \theta -\sin { \theta  } $$ at $$\theta = \dfrac { \pi  }{ 2 } $$ is

Consider the following in respect of the function $$f(x) = \left\{\begin{matrix}2+ x, & x \geq 0\\ 2 - x, & x < 0\end{matrix}\right.$$
1. $$\displaystyle \lim_{x \rightarrow 1} f(x)$$ does not exist.
2. f(x) is differentiable at x = 0.
3. f(x) is continuous at x = 0.
Which of the above statements is/are correct?