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Every continuous function is differentia...

Every continuous function is differentiable.

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Show that |x-5| is continuous but not differentiable at x =5.

Show that the function f(x) = {:{(x^n sin(1/x), x ne 0),(0, x = 0):} is continuous but not differentiable at x= 0.

Show that f(x) = |x - 5| is continuous but not differentiable at x = 5.

The function f(x) = |x| + |x-1| + |x-2| is continuous but not differentiable at for all x in R x=-1 and x=1

The function f(x)=sqrt(1-sqrt(1-x^2)) a. has its domain -1 le x le 1 b. has finite one sided derivates at the point x = 0 c. is continuous and differentiable at x = 0 d. is continuous but not differentiable at x = 0

Let alpha in R . Prove that a function f: RtoR is differentiable at alpha if and only if there is a function g:RtoR which is continuous at alpha and satisfies f (x) -f(alpha) = g (x) (x-alpha), AA x in R.

If f(x) = 3(2x + 3)^(2//3) + 2x + 3 , then: (a) f(x) is continuous but not differentiable at x = - (3)/(2) (b) f(x) is differentiable at x = 0 (c) f(x) is continuous at x = 0 (d) f(x) is differentiable but not continuous at x = - (3)/(2)

The composition of two continuous function is a continuous function.

Show that the function 'f' defined as follows, is continuous at x = 2, but not differentiable there at: f(x) = {:{(3x-2,0 2):}

if f(x) ={{:( (x log cos x)/( log( 1+x^(2) )), x ne 0) ,( 0, x=0):} a. f is continuous at x = 0 b. f is continuous at x = 0 but not differentiable at x = 0 c. f is differentiable at x = 0 d. f is not continuous at x = 0

PSEB-APPLICATION OF DERIVATIVES-Exercise
  1. Every continuous function is differentiable.

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  2. Find the rate of change of the area of a circle with respect to its ra...

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  3. Find the rate of change of the area of a circle with respect to its ra...

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  4. The volume of a cube is increasing at the rate of 8 cm^3/s. How fast i...

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  5. The radius of a circle is increasing uniformly at the rate of 3 cm/s. ...

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  6. An edge of a variable cube is increasing at the rate of 3 cm/s. How fa...

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  7. A stone is dropped into a quiet lake and waves move in circles at the ...

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  8. The radius of a circle is increasing at the rate of 0.7 cm/s. What is ...

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  9. The length 'x' of a rectangle is decreasing at the rate of 5 cm per mi...

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  10. The length 'x' of a rectangle is decreasing at the rate of 5 cm per mi...

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  11. A balloon, which always remains spherical on inflation, is being infla...

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  12. A balloon, which always remains spherical has a variable radius. Find ...

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  13. A ladder 5 m long is leaning against a wall. The bottom of the ladder ...

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  14. A particle moves along the curve 6y = x^3+2. Find the points on the cu...

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  15. The radius of an air bubble is increasing at the rate of 1/2 cm/s. At...

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  16. A balloon, which always remains spherical, has a variable diameter 3/2...

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  17. Sand is pouring from a pipe at the rate of 12 cubic cm./sec. The falli...

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  18. The total cost C(x) in Rupees associated with the production of x unit...

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  19. The total revenue in Rupees received from the sale of x units of a pro...

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  20. Find the rate of change of the area of a circle with respect to its ra...

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  21. The total revenue in Rupees received from its sale of x units of a pro...

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