O'Reilly logo

FUNDAMENTALS OF MATHEMATICS DIFFERENTIAL CALCULUS by Sanjay Mishra

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

TEXTUAL EXERCISE–4: (SUBJECTIVE)
  1. Let f(x) = sin(cos x), then check whether it is increasing or decreasing in images
  2. Show that x3 – 3x2 – 9x + 20 is positive for all values of x > 4.
  3. Solve for x: (x + 3)5 – (x – 1)5 ≥ 244
  4. Find range of
    a. xx b. log[(sin x)sin x + 1]
  5. Show that ex – 1 + x = 2 has only one real root.

Answer Keys

1. Decreasing

3. [0, ∞)

4. (a) [e–1/e, ∞)

(b) [log(e–1/e + 1), log 2]

TEXTUAL EXERCISE–4: (OBJECTIVE)
  1. If f: ℝ → ℝ is decreasing and g : ℝ → ℝ is increasing then which of the following functions is increasing
    a. f o f b. g o g
    c. f o g d. g o f
  2. The function is increasing function of x if
    a. ab > cd b. ad > ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required