Let fx=[ x sin1/x , x ≠ 0; k , x=0 ].Then f is continuous at x=0 if,

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Standard XII

Mathematics

Graphical Interpretation of Derivative

Let fx=[ x si...

Question

k = 0

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k = 1

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k = 1/x

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k = 2

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Solution

The correct option is A
k = 0

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Similar questions

Q. Find the values of k for which the roots are real and equal in each of the following equations:

(i)

k x^{2} + 4 x + 1 = 0

(ii)

k x^{2} - 2 \sqrt{5} x + 4 = 0

(iii)

3 x^{2} - 5 x + 2 k = 0

(iv)

4 x^{2} + k x + 9 = 0

(v)

2 k x^{2} - 40 x + 25 = 0

(vi)

9 x^{2} - 24 x + k = 0

(vii)

4 x^{2} - 3 k x + 1 = 0

(viii)

x^{2} - 2 (5 + 2 k) x + 3 (7 + 10 k) = 0

(ix)

(3 k + 1) x^{2} + 2 (k + 1) x + k = 0

(x)

k x^{2} + k x + 1 = - 4 x^{2} - x

(xi)

(k + 1) x^{2} + 2 (k + 3) x + (k + 8) = 0

(xii)

x^{2} - 2 k x + 7 k - 12 = 0

(xiii)

(k + 1) x^{2} - 2 (3 k + 1) x + 8 k + 1 = 0

(xiv)

(2 k + 1) x^{2} + 2 (k + 3) x + (k + 5) = 0

(xvii)

4 x^{2} - 2 (k + 1) x + (k + 4) = 0

(xviii)

4 x^{2} - 2 (k + 1) x + (k + 1) = 0

Q. Find the values of k for which the following equations have real and equal roots:
(i)

x^{2} - 2 (k + 1) x + k^{2} = 0

(ii)

k^{2} x^{2} - 2 (2 k - 1) x + 4 = 0

(iii)

(k + 1) x^{2} - 2 (k - 1) x + 1 = 0

(iv)

x^{2} + k (2 x + k - 1) + 2 = 0

Q. The system of equations

k x + (k + 1) y + (k - 1) z = 0

(k + 1) x + k y + (k + 2) z = 0

(k - 1) x + (k + 2) y + k z = 0

has a non-trivial solution for

Find the values of k for which the roots are real and equal in each of the following equations.
$(i) k x^{2} + 4 x + 1 = 0 (i i) k x^{2} - 2 \sqrt{5} x + 4 = 0 (i i i) 3 x^{2} - 5 x + 2 k = 0 (i v) 4 x^{2} + k x + 9 = 0 (v) 2 k x^{2} - 40 x + 25 = 0 (v i) 9 x^{2} - 24 x + k = 0 (v i i) 4 x^{2} - 2 k x + 1 = 0 (v i i i) x^{2} - 2 (5 + 2 k) x + 3 (7 + 10 k) = 0 (i x) (3 k + 1) x^{2} + 2 (k + 1) x + k = 0 (x) k x^{2} + k x + 1 = - 4 x^{2} - x (x i) (k + 1) x^{2} + 2 (k + 3) x (k + 8) = 0 (x i i) x^{2} - 2 k x + 7 k - 12 = 0 (x i i i) (k + 1) x^{2} - 2 (3 k + 1) x + 8 k + 1 = 0 (x i v) 5 x^{2} - 4 x + 2 + k (4 x^{2} 1 - 2 x - 1) = 0 (x v) (4 - k) x^{2} + (2 k + 4) x + (8 k + 1) = 0 (x v i) (2 k + 1) x^{2} + 2 (k + 3) x + (k + 5) = 0 (x v i i) 4 x^{2} - 2 (k + 1) x + (k + 4) = 0 (x v i i i) 4 x^{2} - 2 (k + 1) x + (k + 1) = 0$

Q. Let x > 0, y > 0, z > 0 are respectively the

2^{n d}, 3^{r d}, 4^{t h},

terms of a G.P and

Δ = ∣ ∣ ∣ ∣ ∣ \begin{matrix} x^{k} & x^{k + 1} & x^{k + 2} y^{k} & y^{k + 1} & y^{k + 2} z^{k} & z^{k + 1} & z^{k + 2} \end{matrix} ∣ ∣ ∣ ∣ ∣ = (r - 1)^{2} (1 - \frac{1}{r^{2}})

(where r is the common ratio) then

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The correct option is A k = 0

The correct option is A
k = 0