Continuity of Piecewise Functions — Determining Continuity

Find the value of k for which the function 𝐟(𝐱)={((𝟏−𝐜𝐨𝐬𝐱)/(𝟐𝐱^𝟐 ), 𝐢𝐟 𝐱≠𝟎 𝐤, 𝐢𝐟

Q) The value of k for which f(x)={(sin7x/5x,x≠0 k,x=0) is continuous at x=0 is

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Q) Find the value of k, so that f(x)={ ((kcos x)/(𝜋−2x),if x≠𝜋/2 3, if x=𝜋/2) is contin

Q) If 𝑓(𝑥)={(3𝑥−2, 0≤𝑥≤1 2𝑥^2+𝑎𝑥, 1≤𝑥≤2) is continuous for 𝑥∈(0,2), then a is equal to

Find the values of 𝛌 if the function 𝐟(𝐱)={((〖𝐬𝐢𝐧^𝟐 𝛌𝐱)/𝐱^𝟐 , 𝐢𝐟 𝐱≠𝟎 𝟏, 𝐢𝐟 𝐱=𝟎)

Q) For the curve √x+√y=1, find the value of dy/dx at the point (1/9,1/9)

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