Continuity of Piecewise Functions — Determining Continuity

Q) If tan^(−1) 𝑥=𝑦, then 𝑑𝑦/𝑑𝑥 is equal to #continuity_and_differentiability #maths #cbse

Q) If 2cos^(−1) x=y, then dy/dx is #continuity_and_differentiability #maths #cbsemaths #cbse2027

Q) Determine a and b if f(x) is a continuous function, where 𝑓(𝑥)={(2, ≤3 𝑎𝑥+𝑏, 3=𝑥=5 5, 𝑥≥5)

Q) 𝑑/𝑑𝑥 [ 𝑐𝑜𝑠 ( 𝑙𝑜𝑔 𝑥+ 𝑒^(𝑥 ) ) ] 𝑎𝑡 𝑥=1 #cbse2027 #maths #cbse #cbseclass12

Q) If 𝑦=sin^(−1) {𝑥/√(𝑥^2+1)}, find 𝑑𝑦/𝑑𝑥. #cbseclass12 #maths #cbse2026 #cbse2027 #cbse

Q) Show that the derivative of tan^(−1) (sec𝑥+tan𝑥),[−𝜋/2𝑥𝜋/2] with respect to x is equal to 1

Q)If y = cosec ( 𝑐𝑜𝑡^(−1) 𝑥 ) , then prove that √(1+ 𝑥^2 ) (𝑑 𝑦)/(𝑑 𝑥 ) −𝑥=0 .

Q) If 𝑦=logtan(𝜋/4+𝑥/2), then prove that 𝑑𝑦/𝑑𝑥−sec𝒙=𝟎 #cbse2027 #maths #differentiation

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If a function defined by 𝑓(𝑥)={(𝑘𝑥+1, 𝑥≤𝜋 cos𝑥 ,𝑥=𝜋) is continuous at 𝑥=𝜋, then the val

Q) Differential of 𝑒^(𝑒^𝑥 ) with respect to x is #continuityanddifferentiabilityclass12 #cbse202

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