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Examine whether the function f given by ...

Examine whether the function f given by `f(x)=x^2` is continuous at `x = 0`.

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To determine whether the function \( f(x) = x^2 \) is continuous at \( x = 0 \), we need to follow these steps: ### Step 1: Find the functional value at \( x = 0 \) We start by calculating the value of the function at \( x = 0 \): \[ f(0) = 0^2 = 0 \] ...
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NCERT-CONTINUITY AND DIFFERENTIABILITY-SOLVED EXAMPLES
  1. Show that the function defined by f(x) = sin(x^2)is a continuous func...

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  2. Prove that the function defined by f(x) = t a n xis a continuous func...

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  3. Examine whether the function f given by f(x)=x^2 is continuous at x =...

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  4. Discuss the continuity of the function f given by f(x) = |x| at x = 0.

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  5. Check the continuity of the function f given by f(x) = 2x + 3 at x = ...

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  6. Prove that the identity function on real numbers given by f(x) = x is...

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  7. Is the function defined by f(x) = |x|, a continuous function?

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  8. Show that the function f given by f(x)={x^3+3ifx!=0 ;1ifx=0 is not ...

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  9. Check the points where the constant function f(x) = kis continuous.

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  10. Discuss the continuity of the function/given by f(x)=x^3+x^2-1.

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  11. Discuss the continuity of the function f defined by f(x)=1/x , x!=0.

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  12. If y= A sin x+ B cos x, then prove that (d^2y)/(dx^2)+y=0.

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  13. Find (d^2y)/(dx^2), if y=x^3+tanx.

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  14. Find (dy)/(dx), if x^(2/3)+y^(2/3)=a^(2/3).

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  15. Find (dy)/(dx), if x=a(theta+sintheta), y=a(1-costheta).

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  16. Find (dy)/(dx), if x=a t^2, y=2a t.

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  17. Find (dy)/(dx), if x=acostheta,y=asintheta.

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  18. Find (dy)/(dx), if y^x+x^y+x^x=a^b.

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  19. Differentiate x^(sinx), x >0w.r.t. x.

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  20. Differentiate a^xw.r.t. x, where a is a positive constant.

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