Use Coupon: CART20 and get 20% off on all online Study Material

Total Price: R

There are no items in this cart.
Continue Shopping
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 400 off


Suppose f is a function that satisfies the equation f (x+y) = f(x)+f(y)+x2y+xy2 for all real real numbers x and y.if limit {f(x)/x} as x →0 is equal to 1, then

a) f(x)>0 for x>0 and f(x)<0 for x<0              2)  f1(0)=1    

3)f11(0)=1  4)f111(x) is a constant function


6 years ago


Answers : (1)


Dear Aman V Ranga Reddy,


Differntiating With Respect to X keeping y constant we get, f′(x+y)=f′(x)+2xy+y²...............(1)

Now limit{f(x)/x) as x tends to 0 is=1 Hence f′(0)=1.............(2)

Putting x=0 in eq (1) we get


f′(y)=1+y² (which is true as we put y=0 it satifies eq 1)



Hence options 2 and 4 are correct

Please feel free to post as many doubts on our discussion forum as you can. If you find any question
Difficult to understand - post it here and we will get you the answer and detailed solution very quickly. We
are all IITians and here to help you in your IIT JEE preparation.

All the best Aman V Ranga Reddy !!!



Askiitians Experts
Soumyajit Das IIT Kharagpur

6 years ago

Post Your Answer

Other Related Questions on Differential Calculus

differentiate (x+2)sin3x/ x 3 +cot 2 x with respect to x
Dear Student, In this problem you will need to use the formula for differentiation of two functions in division i.e. d/dx (1/2) = 2(d/dx (1)) – 1 (d/dx(2)) / (2 2 ) . Also you need to...
Vijay Mukati 7 months ago
) . Also you need to apply chain rule simultaneously.Thanks.or 2 n this problem you will need to use the formula for differentiation of two functions in division i.e. d/dx (1/2) = 2(d/dx...
siva prasad reddy 7 months ago
Can anyone solve this problem and provide the solution
as x tends to infinty x= x-1 =x+1 f(x)= 1/2( f(x)+ 3/f(x)) f(x)/2 = 3/2f(x) f(x) 2 = 3 Hence b
Harsh Patodia 6 months ago
the answer for your question is square root of three.that will come by solving all the best for your bright future
Prabhakar ch 6 months ago
e x l og a + e alogx +e aloga
since we can write e xlog a =e log a^x =a x so the required answer is a x +x a +a a
Revti Raman one year ago
Let abc be sides of triangle . No two are equal and € belongs to real numbers.If roots of x.x +2(a+b+c)x+3€(ab+bc+ca)=0 are real. Then range of€=?
In triangles we have the inequality which can be written as The left inequality arises from and the right inequality from the triangle inequalities squared i.e. and summing up. If then the...
mycroft holmes 2 months ago
For roots to be real its Discriminant should be greater than equal to zero. It should not be imaginary. Hence, 4(a+b+c)^2 – 12 €(ab+bc+ca) greater than equal to zero.
Vikas TU 2 months ago
what is meant by integration????????????????????????/
integration is the act of integrating,it is the act of bringing together smaller components into a single or small type of functions as only one..........
nandini 6 months ago
Integration is the act of bringing together smaller components into a single system that functions as one.
Vaishnavi Patel 6 months ago
how to obtain your math notes.
You can purchace online from its website. Thanks.
Vijay Mukati one year ago
certain notes are available free. you can also vist some other sites, where free notes of each subject is available. please surf the web to find such sites. it is better to get free notes...
vindhya one year ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,750 off

Get extra R 400 off

More Questions On Differential Calculus

Ask Experts

Have any Question? Ask Experts

Post Question

Answer ‘n’ Earn
Attractive Gift
To Win!!!
Click Here for details