The function f(x) = x - 2 + x is
differentiable at both x = 2 and x = 0
differentiable at x = 2 but not at x = 0
continuous at x = 2 but not at x = 0
continuous at both x = 2and x = 0
If y = tan-1x2 - 1, then the ratio d2ydx2 : dydx is
xx2 - 11 - 2x2
1 - 2x2xx2 - 1
1 + 2x2xx2 + 1
xx2 + 11 - 2x2
If f(x) = fx = logxx - 1, if x ≠ 1k, if x ≠ 1 is continuous at x = 1, then the value of k is
0
- 1
1
e
If r = aeθcotα where a and α, are real numbers, then d2rdθ2 - 4rcot2α is
r
1r
D.
Given, r = aeθcotα ...iDifferentiating w.r.t. θ,12rdrdθ = acotα . eθcotα⇒ drdθ = 2ar cotα eθcotα⇒ drdθ = 2a . aeθcotα . cotα . eθcotα ∵ from Eq. (i)⇒ drdθ = 2a2 cotα . α . e2θcotαAgian r differentiating w.r.t.θd2rdθ2 = 2a2 cotα . e2θcotα . 2cotαd2rdθ2 = 4a2cot2α . e2θcotαd2rdθ2 = 4cot2α . aeθcotα2d2rdθ2 = 4cot2α . r2 ∵ from Eq. (i)d2rdθ2 - 4rcot2α = 0
The derivative of tan-1sinx1 + cosx with respect to tan-1cosx1 + sinx is
2
- 2
ddxcoscot-12 + x2 - x is
14
12
- 12
- 34
If y = loge1 + x + x2 + .. ∞, then dydx is equal to
11 + x2
11 - x2
- 11 + x2
- 11 - x2
Length of the subtangent at (x1, y1) on xnym = am + n, m, n > 0, is
nmx1
mnx1
nmy1
If y = tan-111 + x + x2 + tan-11x2 + 2x + 3 + tan-11x2 + 5x + 7 + ... n terms, then y'(0) is
π2
2n1 + n2
n21 + n2
- n21 + n2
If f(x) = x2 - a + 2x + ax - 2, x ≠ 22, x = 2 is continuous at x = 2, then at x = 2, then the value of a is
- 6