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Prove that the function f given by f(x) ...

Prove that the function f given by `f(x) = x^2-x+1` is neither strictly increasing nor decreasing on `(– 1, 1)`.

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MODERN PUBLICATION-MOCK TEST-1-EXERCISE
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  2. If x sin (a+y) + sin a cos (a+y) = 0, then prove that : dy/dx = (sin^...

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  3. Prove that the function f given by f(x) = x^2-x+1 is neither strictly ...

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  4. Find the approximate change in the volume V of a cube of side x metres...

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  5. Evaluate int(pi//6)^(pi//3) ((1)/(1+sqrttanx dx

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  6. Solve the following differential equations x dy + ( y - x^3) dx =0

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  7. Find the value of 'lambda' such that the vectors : 3hati+lambda hatj+5...

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  8. tan^-1 frac{1}{5} + tan^-1 frac{1}{7} + tan^-1 frac {1}{3} + tan^-1 fr...

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  9. Prove that : tan^-1((cosx)/(1+sinx)) = pi/4 - x/2, x in (-pi/2,pi/2)

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  10. Show that if A = [[cos theta, sin theta],[-sin theta, cos theta]], th...

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  11. Using the properties of determinant, show that :|[a^2+1,ab,ac],[ab,b^2...

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  12. The funtion f(x) is defined as follows: f(x) = {:{(x^2+ax+b,0lex<2),...

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  13. Evalute : int(5x+3)/sqrt(x^2+4x+10)dx

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  14. By using the properties of definite integrals, evaluate the integral: ...

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  15. Solve: dy/dx+(2x)/(x^2+1)y=1/(x^2+1)^2, y(0)=0.

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  16. Find the shortest distance between the lines: vecr=6hati+2hatj+2hatk+l...

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  17. Find the equation of the plane passing through the intersection of the...

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  18. A problem in Mathematics is given the three students whose chances of ...

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  19. A problem in Mathematics is given the three students whose chances of ...

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  20. If A and B are subsets of the universal set U, then show that A⊂ A∪ B...

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