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Definition : A function f ( x ) is called differentiable at x = a if f ′ ( x ) exists & f ( x ) is called differentiable onto an interval if the derivative present for each of the

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For the given function recognize the intervals where the function is increasing and decreasing and the intervals where the function is concave up & concave down. Utilizes this info

Show that the function f is one-one but not onto, Consider the function f: ...

Consider the function f: N → N, where N is the set of natural numbers, defined by f(n) = n 2 +n+1. Show that the function f is one-one but not onto. Ans: To prove that f is one

What is venn diagram, The diagrams drawn to given sets are called as Venn d...

The diagrams drawn to given sets are called as Venn diagrams or Eule -Venn diagrams. Here given the universal set U by points within rectangle and the subset A of the set U given b

Homomorphism, Let G be a group acting on a set X. The action is called fait...

Let G be a group acting on a set X. The action is called faithful if for any g ≠ 1 ∈ G there exists an x ∈ X such that gx ≠ x. That is, only the identity fi xes everything. Prov

A fire in a building b is reported on telephone, A fire in a building B is ...

A fire in a building B is reported on telephone to two fire stations P and Q, 10km apart from each other on a straight road.  P observes that the fire is at an angle of 60 o to th

John 47 out of 86 free-throws who best free-throw shooter, Michael made 19 ...

Michael made 19 out of 30 free-throws this basketball season. Larry's freethrow average was 0.745 and Charles' was 0.81. John made 47 out of 86 free-throws. Who is the best free-th

Introduction to multiplication and division, INTRODUCTION :  When a Class ...

INTRODUCTION :  When a Class 5 child was given the problem 'If I paid Rs. 60 for 30 pencil boxes, how much did b pencil box cost?', he said it would be 60 x 30 = 1800. This

Estimate the distance to this star, To find the distance to nearby stars, t...

To find the distance to nearby stars, the method of parallax is used. The idea is to find a triangle with the star at one vertex and with a base as large as possible. To do this, t

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