Limit Continuity And Differentiability

Limit Continuity And Differentiability Ques 1
Limit Continuity And Differentiability Ques 2
Limit Continuity And Differentiability Ques 3
Limit Continuity And Differentiability Ques 4
Limit Continuity And Differentiability Ques 5
Limit Continuity And Differentiability Ques 6
Limit Continuity And Differentiability Ques 7
Limit Continuity And Differentiability Ques 8
Limit Continuity And Differentiability Ques 9
Limit Continuity And Differentiability Ques 10
Limit Continuity And Differentiability Ques 11
Limit Continuity And Differentiability Ques 12
Limit Continuity And Differentiability Ques 13
Limit Continuity And Differentiability Ques 14
Limit Continuity And Differentiability Ques 15
Limit Continuity And Differentiability Ques 16
Limit Continuity And Differentiability Ques 17
Limit Continuity And Differentiability Ques 18
Limit Continuity And Differentiability Ques 19
Limit Continuity And Differentiability Ques 20
Limit Continuity And Differentiability Ques 21
Limit Continuity And Differentiability Ques 22
Limit Continuity And Differentiability Ques 23
Limit Continuity And Differentiability Ques 24
Limit Continuity And Differentiability Ques 25
Limit Continuity And Differentiability Ques 26
Limit Continuity And Differentiability Ques 27
Limit Continuity And Differentiability Ques 28
Limit Continuity And Differentiability Ques 29
Limit Continuity And Differentiability Ques 30
Limit Continuity And Differentiability Ques 31
Limit Continuity And Differentiability Ques 32
Limit Continuity And Differentiability Ques 33
Limit Continuity And Differentiability Ques 34
Limit Continuity And Differentiability Ques 35
Limit Continuity And Differentiability Ques 36
Limit Continuity And Differentiability Ques 37
Limit Continuity And Differentiability Ques 38
Limit Continuity And Differentiability Ques 39
Limit Continuity And Differentiability Ques 40
Limit Continuity And Differentiability Ques 41
Limit Continuity And Differentiability Ques 42
Limit Continuity And Differentiability Ques 43
Limit Continuity And Differentiability Ques 44
Limit Continuity And Differentiability Ques 45
Limit Continuity And Differentiability Ques 46
Limit Continuity And Differentiability Ques 47
Limit Continuity And Differentiability Ques 48
Limit Continuity And Differentiability Ques 49
Limit Continuity And Differentiability Ques 50
Limit Continuity And Differentiability Ques 51
Limit Continuity And Differentiability Ques 52
Limit Continuity And Differentiability Ques 53
Limit Continuity And Differentiability Ques 54
Limit Continuity And Differentiability Ques 55
Limit Continuity And Differentiability Ques 56
Limit Continuity And Differentiability Ques 57
Limit Continuity And Differentiability Ques 58
Limit Continuity And Differentiability Ques 59
Limit Continuity And Differentiability Ques 60
Limit Continuity And Differentiability Ques 61
Limit Continuity And Differentiability Ques 62
Limit Continuity And Differentiability Ques 63
Limit Continuity And Differentiability Ques 64
Limit Continuity And Differentiability Ques 65
Limit Continuity And Differentiability Ques 66
Limit Continuity And Differentiability Ques 67
Limit Continuity And Differentiability Ques 68
Limit Continuity And Differentiability Ques 69
Limit Continuity And Differentiability Ques 70
Limit Continuity And Differentiability Ques 71
Limit Continuity And Differentiability Ques 72
Limit Continuity And Differentiability Ques 73
Limit Continuity And Differentiability Ques 74
Limit Continuity And Differentiability Ques 75
Limit Continuity And Differentiability Ques 76
Limit Continuity And Differentiability Ques 77
Limit Continuity And Differentiability Ques 78
Limit Continuity And Differentiability Ques 79
Limit Continuity And Differentiability Ques 80
Limit Continuity And Differentiability Ques 81
Limit Continuity And Differentiability Ques 82
Limit Continuity And Differentiability Ques 83
Limit Continuity And Differentiability Ques 84
Limit Continuity And Differentiability Ques 85
Limit Continuity And Differentiability Ques 86
Limit Continuity And Differentiability Ques 87
Limit Continuity And Differentiability Ques 88
Limit Continuity And Differentiability Ques 89
Limit Continuity And Differentiability Ques 90
Limit Continuity And Differentiability Ques 91
Limit Continuity And Differentiability Ques 92
Limit Continuity And Differentiability Ques 93
Limit Continuity And Differentiability Ques 94
Limit Continuity And Differentiability Ques 95
Limit Continuity And Differentiability Ques 96
Limit Continuity And Differentiability Ques 97
Limit Continuity And Differentiability Ques 98
Limit Continuity And Differentiability Ques 99
Limit Continuity And Differentiability Ques 100
Limit Continuity And Differentiability Ques 101
Limit Continuity And Differentiability Ques 102
Limit Continuity And Differentiability Ques 103
Limit Continuity And Differentiability Ques 104
Limit Continuity And Differentiability Ques 105
Limit Continuity And Differentiability Ques 106
Limit Continuity And Differentiability Ques 107
Limit Continuity And Differentiability Ques 108
Limit Continuity And Differentiability Ques 109
Limit Continuity And Differentiability Ques 110
Limit Continuity And Differentiability Ques 111
Limit Continuity And Differentiability Ques 112
Limit Continuity And Differentiability Ques 113
Limit Continuity And Differentiability Ques 114
Limit Continuity And Differentiability Ques 115
Limit Continuity And Differentiability Ques 116
Limit Continuity And Differentiability Ques 117
Limit Continuity And Differentiability Ques 118
Limit Continuity And Differentiability Ques 119
Limit Continuity And Differentiability Ques 120
Limit Continuity And Differentiability Ques 121
Limit Continuity And Differentiability Ques 122
Limit Continuity And Differentiability Ques 123
Limit Continuity And Differentiability Ques 124
Limit Continuity And Differentiability Ques 125
Limit Continuity And Differentiability Ques 126
Limit Continuity And Differentiability Ques 127
Limit Continuity And Differentiability Ques 128
Limit Continuity And Differentiability Ques 129
Limit Continuity And Differentiability Ques 130
Limit Continuity And Differentiability Ques 131
Limit Continuity And Differentiability Ques 132
Limit Continuity And Differentiability Ques 133
Limit Continuity And Differentiability Ques 134
Limit Continuity And Differentiability Ques 135
Limit Continuity And Differentiability Ques 136
Limit Continuity And Differentiability Ques 137
Limit Continuity And Differentiability Ques 138
Limit Continuity And Differentiability Ques 139
Limit Continuity And Differentiability Ques 140

Limit Continuity And Differentiability Ques 28

Let $f$ be a twice differentiable function such that

$f^{\prime \prime}(x)=-f(x), f^{\prime}(x)=g(x)$ and

$ h(x)=[f(x)]^2+[g(x)]^2 $

Find $h(10)$, if $h(5)=11$.

(1983, 3M)

Show Answer

Solution: Given, $h(x)=[f(x)]^2+[g(x)]^2$

$ \begin{aligned} & \Rightarrow \quad h^{\prime} x=2 f(x) \cdot f^{\prime}(x)+2 g(x) \cdot g^{\prime}(x) \\ & =\quad 2[f(x) \cdot g(x)-g(x) \cdot f(x)] \\ & =\quad 0 \quad\left[\because f^{\prime}(x)=g(x) \text { and } g^{\prime}(x)=-f(x)\right] \\ \end{aligned} $

$\therefore \quad h(x)$ is constant.

$ \Rightarrow \quad h(10)=h(5)=11 $

Limit Continuity And Differentiability

Limit Continuity And Differentiability Ques 28

Solution: Given, $h(x)=[f(x)]^2+[g(x)]^2$

Table of Contents

Menu