RD Sharma Solutions Class 12 Maths Chapter 15 Ex 15...RD Sharma Solutions Class 12 Maths Chapter 15...
Transcript of RD Sharma Solutions Class 12 Maths Chapter 15 Ex 15...RD Sharma Solutions Class 12 Maths Chapter 15...
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RD Sharma
Solutions
Class 12 Maths
Chapter 15
Ex 15.2
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Mean Value Theorems Ex 15.2 Q1(i)
Mean Value Theorems Ex 15.2 Q1(ii)
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Mean Value Theorems Ex 15.2 Q1(iii)
Mean Value Theorems Ex 15.2 Q1(iv)
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Mean Value Theorems Ex 15.2 Q1(v)
Mean Value Theorems Ex 15.2 Q1(vi)
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Mean Value Theorems Ex 15.2 Q1(vii)
Mean Value Theorems Ex 15.2 Q1(viii)
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Mean Value Theorems Ex 15.2 Q1(ix)
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Mean Value Theorems Ex 15.2 Q1(x)
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Mean Value Theorems Ex 15.2 Q1(xi)
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Mean Value Theorems Ex 15.2 Q1(xii)
Mean Value Theorems Ex 15.2 Q1(xiii)
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Mean Value Theorems Ex 15.2 Q1(xiv)
Mean Value Theorems Ex 15.2 Q1(xv)
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Mean Value Theorems Ex 15.2 Q1(xvi)
Mean Value Theorems Ex 15.2 Q2
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Mean Value Theorems Ex 15.2 Q3
Mean Value Theorems Ex 15.2 Q4
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Mean Value Theorems Ex 15.2 Q5
Mean Value Theorems Ex 15.2 Q6
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Mean Value Theorems Ex 15.2 Q7
Mean Value Theorems Ex 15.2 Q8
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Mean Value Theorems Ex 15.2 Q9
Mean Value Theorems Ex 15.2 Q10
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Mean Value Theorems Ex 15.2 Q11
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Consider the function as
f (x) = tanx, {xe[a,b] such that0<a<b<%}
We know that tanx is continuous and differentiable in ( D, �), so, Lagrange's mean value
theorem is ap plicable on (a,b) , so there exists a point c such that,
⇒
Now,
⇒
⇒
⇒
f' (c) = f (b) - f(a)
b-a2 tanb - tan a sec c =
b
ce(a,b) a<c<b
-a
sec2 a < sec2 c < sec2 b
sec a < ----- < sec-2 (tan b - tan a) _2 b b - a
Using equation (i) ,
(b - a) sec 2 a< (tan b - tan a)< (b - a) sec 2 b
---(i)