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Continuity & Differentiability · Question 63 of 125

At how many points of (0, 5) is this charge not continuous?

Question 63

EasyOriginal question

A courier charges C(w)=40+20[w]C(w) = 40 + 20[w] rupees for a parcel of weight ww kg, where 0<w<50 < w < 5 and [w][w] is the greatest integer not more than ww.

At how many points of (0,5)(0, 5) is this charge not continuous?

Options for question 63

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. [w][w] jumps by 1 at each integer, so CC jumps by 20 there.

  2. The integers inside (0,5)(0, 5) are 1, 2, 3, 4: 4 points.

Worth noting

5 counts w=5w = 5 as well, which the interval leaves out.

Concept
Discontinuities of the greatest integer function
Typical time
90 s
Your time
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The rule this testsContinuous functions
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