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2.g. limit
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2.g. limit
2.f.
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2.f.
2.e. x lim 0 (x+1)^8 - 1 / (x+1)^2 - 1
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2.e. x lim 0 (x+1)^8 - 1 / (x+1)^2 - 1
2.d. x lim a x^2/3 - a^2/3 / x-a
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2.d. x lim a x^2/3 - a^2/3 / x-a
2.c. x lim a x^5-a^5 / x^4-a^4
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2.c. x lim a x^5-a^5 / x^4-a^4
2. b. x lim 1 x^2- 5x +4 /x^2 +2x -3
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2. b. x lim 1 x^2- 5x +4 /x^2 +2x -3
1.d. x lim 1 x^3 - 1 / x-1
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1.d. x lim 1 x^3 - 1 / x-1
26. y lim x ysecy -xsecx / y-x
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26. y lim x ysecy -xsecx / y-x
25. xlimθ x tanx -θ tanθ / x-θ
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25. xlimθ x tanx -θ tanθ / x-θ
24. x lim θ xcotθ - θ cotx / x-θ
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24. x lim θ xcotθ - θ cotx / x-θ
23. xlim θ xsinθ- θsinx / x-θ
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23. xlim θ xsinθ- θsinx / x-θ
5.f. Using the properties of determinant, prove that:
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5.f. Using the properties of determinant, prove that:
5.c. Using the properties of determinant, prove that:
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5.c. Using the properties of determinant, prove that:
5.b. Using the properties of determinant, prove that:
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5.b. Using the properties of determinant, prove that:
5.d. Using the properties of determinant, prove that:
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5.d. Using the properties of determinant, prove that:
5.e. Using the properties of determinant, prove that:
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5.e. Using the properties of determinant, prove that:
7. If the roots of equation a(b-c)x^2 +b(c-a)x +c(a-b) =0 be equal then show that a,b,c are in H.P.
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7. If the roots of equation a(b-c)x^2 +b(c-a)x +c(a-b) =0 be equal then show that a,b,c are in H.P.
6. If the roots of the equation (a^2+b^2)x^2 - 2(ac+bd)x +(c^2+d^2) = 0 are equal then prove that
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6. If the roots of the equation (a^2+b^2)x^2 - 2(ac+bd)x +(c^2+d^2) = 0 are equal then prove that
5. Show that the roots of the equation (a^2-bc) x^2 + 2(b^2-ca)x + (c^2-ab) =0 will be equal if
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5. Show that the roots of the equation (a^2-bc) x^2 + 2(b^2-ca)x + (c^2-ab) =0 will be equal if
4. If the equation (1+m^2)x^2 + 2mcx + c^2 - a^2 = 0 has equal roots, show that c^2 = a^2 (1+m^2)
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4. If the equation (1+m^2)x^2 + 2mcx + c^2 - a^2 = 0 has equal roots, show that c^2 = a^2 (1+m^2)
3.b. Find the value of k so that the equation x^2 -(2k-1)x - (k-1) =0 has equal roots.
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3.b. Find the value of k so that the equation x^2 -(2k-1)x - (k-1) =0 has equal roots.
3.a) Find the value of k so that the equation x² + (k+2)x +2k = 0 has equal roots.
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3.a) Find the value of k so that the equation x² + (k+2)x +2k = 0 has equal roots.
2. For what value of the p will the equation 5x² - px +45 = 0 have the equal roots?
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2. For what value of the p will the equation 5x² - px +45 = 0 have the equal roots?
1.c. 2x² - 12x + 18 = 0
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1.c. 2x² - 12x + 18 = 0
1.e. x² - 16 = 0
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1.e. x² - 16 = 0
1.b. x² -4x - 3 = 0
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1.b. x² -4x - 3 = 0
1.d.4x² + 8x -5 = 0
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1.d.4x² + 8x -5 = 0
1. Determine the nature of the roots of following equations a. x^2 -12x+40 =0
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1. Determine the nature of the roots of following equations a. x^2 -12x+40 =0
3.f.
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3.f.
3.e.
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3.e.