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Class XII_CONTINUITY
INTRODUCTION TO DIFFERENTIABILITY

CONTINUITY:
Previous recorded questions and their links:
Introduction:    • INTRODUCTION TO CONTINUITY  
Q: If f(x)={█(■((x^3+x^2+6x+20)/(x-2)^2 &;x≠2)@■(k& ;x=2))┤ is continuous at x=2, find k.:    • If f(x)={█(■((x^3+x^2+6x+20)/(x-2)^2 &;x≠2...  
Q: For what value of k, will f(x) be continuous at x=5; f(x)={■((x^2-25)/(x-5)&x≠5@k&x=5)┤:    • For what value of k, will f(x) be continuo...  
Q: For what value of k, will f(x) be continuous at x=3 f(x)={■(((x+3)^2-36)/(x-3)&;x≠3@k&;x=3)┤:    • For what value of k, will f(x) be continuo...  
Q: For what value of k, will f(x) be continuous at x=0 f(x)={■((1-cos⁡4x)/x^2 &;x0@k&;x=0@√x/(√(16+√x) -4)&;x0)┤:    • For what value of k, will f(x) be continuo...  
Q: Let f(x)={■(x+a√2 sin⁡x&0≤xπ/4@2x cot⁡x+b&π/4≤x≤π/2@a cos⁡2x-b sin⁡x&π/2x≤π)┤ be continuous in [0,π]. Then find a+b.:    • Let f(x)={■(x+a√2  sin⁡x&0xπ/4@2x cot⁡x+b&...  
Q: Prove that the function f(x)=5x-3 is continuous at x=0, at x=-3 and at x=5.:    • Prove that the function 𝒇(𝒙)=𝟓𝒙−𝟑 is conti...  
Q18: For what value of λ is the function defined by
f(x)={■(λ(x^2-2x)&; if x≤0@4x+1&; if x 0)┤
continuous at x = 0? What about continuity at x=1?:    • Examine the function for continuity. 𝒇(𝒙)=...  
Q3: Examine the function for continuity.
f(x)={■(1/(x-5)&;x≠5)┤    • Examine the function for continuity.𝒇(𝒙)=|...  
Q3: Examine the function for continuity.
f(x)=|x-5|:    • Find all points of discontinuity of 𝒇, whe...  
Q7: Find all points of discontinuity of f, where f is defined by
f(x)={■(|x|+3& if x≤-3@-2x& if -3 x 3@6x+2&if x≥3)┤:    • Find all points of discontinuity of 𝒇, whe...  
Q8: Find all points of discontinuity of f, where f is defined by
f(x)={■(|x|/x&if x≥1@0&if x=0)┤:    • Find the relationship between 𝒂 and 𝒃 so t...  


DIFFERENTIABILITY:





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