Find `("lim")_(x->3)\ f(x),\ w h e r e\ f(x)={4,\ if\ x >3x+1,\ if\ x<3`

Evaluate the following integral: int_2^4f(x)dx ,\ w h e r e\ f(x)={7x+3,\ if\ 1lt=xlt=3 8x ,\ if\ 3lt=xlt=4

find lim_(x rarr3)f(x) where f(x)=4,x>3 and f(x)=x+1,x<3

Find lim_(x to 0)f(x) and lim_(x to 1)f(x) , where f(x)={{:(2x+3",", x le 0), (3(x+1)",", x gt 0):}

Evaluate the following integral: int_0^9f(x)dx ,\ w h e r e\ f(x){sinx ,\ 0lt=xlt=pi//2 1,pi/2lt=xlt=3e^(x-3),\ 3lt=xlt=9

Instead of the usual definition of derivative Df(x), if we define a new kind of derivative D^*F(x) by the formula D*f(x)=lim_(h->0)(f^2(x+h)-f^2(x))/h ,w h e r ef^2(x) mean [f(x)]^2 and if f(x)=xlogx ,then D^*f(x)|_(x=e) has the value (A)e (B) 2e (c) 4e (d) none of these

Find the value of a for which the following function is continuous at a given point. f(x)={(x^2+3x-10)/(x^2+2x-15),\ w h e n\ x!=-5a ,\ w h e n\ x=-5

Let lim_(x to 0) f(x) be a finite number, where f(x) = ("sin" x + ae^(x) + be^(-x) + cln (1 + x))/(x^(3)) a,b,e in R

Let lim_(x to 0) f(x) be a finite number, where f(x) = ("sin" x + ae^(x) + be^(-x) + cln (1 + x))/(x^(3)) a,b,e in R

Let lim_(x to 0) f(x) be a finite number, where f(x) = ("sin" x + ae^(x) + be^(-x) + cln (1 + x))/(x^(3)) a,b,e in R

For int (x -1)/( (x +1 ) ^(3)) e ^(x) dx = e ^(x) f (x) + c , f (x) =(x +1) ^(2).