Limits and Derivatives Test

Result

Limits and Derivatives Test - 1

Score
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Rank
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Weekly Quiz Competition

Question 1
1 / -0

The derivative of f(x) = 1 + x + x²+ x³+ ..... + x¹⁰⁰at x = 1 is

A
5000

B
5050

C
5150

D
5005
Question 2
1 / -0

If f(X) = xⁿ +a x^n-1 + a² x^n-2 +… +a^n-1x + aⁿ for some fixed real number, then f'(x) is equal to

A
a [n (n + 1)/2]

B
a [n² (n + 1)/2]

C
a^n-1[n (n + 1)]

D
a^n-1[n (n + 1)/2]
Question 3
1 / -0

If y = x⁵ cotx, then dy/dx is equal to

A
x⁴ [– x cosec² x + 5 cot x]

B
x⁴ [-x cosec² x – 5 cot x]

C
x⁴ [x cosec² x + 5 cot x]

D
x⁴ [x cosec² x - 5 cot x]
Question 4
1 / -0

If y = a e^mx + b e ^-mx, then y'' is equal to

A
- m² y

B
m²y

C
my₁

D
None of these