Integral Calculus-Fundamental Integrals Involving Functions (KVPY Stream SB-SX (Class 12 & 1st Year BSC) Math): Questions 1 - 2 of 2

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Question number: 1

» Integral Calculus » Fundamental Integrals Involving Functions

Appeared in Year: 2014

MCQ▾

Question

A continuous function f:RR satisfies the equation,

f(x)=x+0xf(t)dt.

Which of the following options is true?

Choices

Choice (4) Response

a.

f(x+y)=f(x)f(y)

b.

f(x+y)=f(x)+f(y)+f(x)f(y)

c.

f(x+y)=f(x)+f(y)

d.

f(x+y)=f(xy)

Question number: 2

» Integral Calculus » Fundamental Integrals Involving Functions

Appeared in Year: 2015

MCQ▾

Question

Let f:RR be a continuous function satisfying,

f(x)+0xtf(t)dt+x2=0,

For all xR . Then –

Choices

Choice (4) Response

a.

limxf(x)=2

b.

f(x) is an odd function

c.

limxf(x)=2

d.

f(x) has more than 1 point in common with the x axis

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