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G Gautam harsolia
Given function is Given function is satisfies for the all real values of x case (i)  k < 0 Hence, function is continuous for all values of x < 0 case (ii)  x = 0 L.H.L at x= 0 R.H.L. at x = 0 L.H.L. = R.H.L. = f(0) Hence, function is continuous at x = 0 case (iii)  k > 0 Hence , function is continuous for all values of x > 0 case (iv) k < 1  Hence , function is...

G Gautam harsolia
Given function is Let g(x) = |x|  and h(x)  = |x+1| Now, g(x) is defined for all real numbers k case(i)  k < 0 Hence, g(x) is continuous when k < 0 case (ii) k > 0 Hence, g(x) is continuous when k > 0 case (iii) k = 0 Hence, g(x) is continuous when k = 0 Therefore, g(x) = |x| is continuous for all real values of x Now, g(x) is defined for all real numbers k case(i)  k <...

G Gautam harsolia
Given function is  f(x) = sin |x| f(x) = h o g  , h(x) = sin x and g(x) = |x| Now, g(x) is defined for all real numbers k case(i)  k < 0 Hence, g(x) is continuous when k < 0 case (ii) k > 0 Hence, g(x) is continuous when k > 0 case (iii) k = 0 Hence, g(x) is continuous when k = 0 Therefore, g(x) = |x| is continuous for all real values of x Now,  h(x) = sin x Let suppose  x...

G Gautam harsolia
Given function is  given function is defined for all values of x f = g o h ,  g(x) = |x| and h(x) = cos x Now, g(x) is defined for all real numbers k case(i)  k < 0 Hence, g(x) is continuous when k < 0 case (ii) k > 0 Hence, g(x) is continuous when k > 0 case (iii) k = 0 Hence, g(x) is continuous when k = 0 Therefore, g(x) = |x| is continuous for all real values of...

G Gautam harsolia
Given function is given function is defined for all real values of x Let x = k + h if  Hence, the function   is a continuous function

G Gautam harsolia
Given continuous function is   The function is continuous so By solving  equation (i) and (ii) a = 2 and b = 1 Hence, values of a and b such that the function defined by          is a continuous function is 2 and 1 respectively

G Gautam harsolia
Given function is When x = 5 For the function to be continuous f(5) = R.H.L. = LH.L. Hence,  the values of k so that the function f is continuous at x= 5 is

G Gautam harsolia
Given function is When x =  For the function to be continuous f() = R.H.L. = LH.L. Hence,  the values of k so that the function f is continuous at x=  is

G Gautam harsolia
Given function is When x = 2 For the function to be continuous f(2) = R.H.L. = LH.L. Hence,  the values of k so that the function f is continuous at x= 2 is

G Gautam harsolia
Given function is When  For the function to be continuous Therefore, the values of k so that the function f is continuous is 6

G Gautam harsolia
Given function is Given function is defined for all real number We, know that if two function g(x) and h(x) are continuous then g(x)+h(x) , g(x)-h(x) , g(x).h(x) allare continuous Lets take g(x) = sin x   and    h(x) = cos x Let suppose  x = c + h if                                                                                                    Hence, function  is a continuous...

G Gautam harsolia
Given function is Given function is defined for all real numbers k when x = 0 Hence, function is continuous at x = 0 when   Hence, the given function is continuous for all points

G Gautam harsolia
Given function is Hence, the function is continuous  Therefore, no point of discontinuity

G Gautam harsolia
We, know that if two function g(x) and h(x) are continuous then  Lets take g(x) = sin x   and    h(x) = cos x Let suppose  x = c + h if                                                                                                    Hence, function  is a continuous function Now, h(x) = cos x Let suppose  x = c + h if                                                              ...

G Gautam harsolia
Given function is Given function is defined for all real number We, know that if two function g(x) and h(x) are continuous then g(x)+h(x) , g(x)-h(x) , g(x).h(x) allare continuous Lets take g(x) = sin x   and    h(x) = cos x Let suppose  x = c + h if                                                                                                    Hence, function  is a continuous...

G Gautam harsolia
Given function is Given function is defined for all real number We, know that if two function g(x) and h(x) are continuous then g(x)+h(x) , g(x)-h(x) , g(x).h(x) allare continuous Lets take g(x) = sin x   and    h(x) = cos x Let suppose  x = c + h if                                                                                                    Hence, function  is a continuous...

G Gautam harsolia
Given function is Given function is defined for all real number We, know that if two function g(x) and h(x) are continuous then g(x)+h(x) , g(x)-h(x) , g(x).h(x) allare continuous Lets take g(x) = sin x   and    h(x) = cos x Let suppose  x = c + h if                                                                                                    Hence, function  is a continuous...

G Gautam harsolia
Given function is Clearly, Given function is defined at x = Hence, the function defined by continuous at x =