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The slope of the tangent to the curve y=...

The slope of the tangent to the curve `y=sqrt(4-x^2)` at the point where the ordinate and the abscissa are equal is `(a) -1` (b) 1 (c) 0 (d) none of these

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A curve y=f(x) passes through point P(1,1) . The normal to the curve at P is a (y-1)+(x-1)=0 . If the slope of the tangent at any point on the curve is proportional to the ordinate of the point, then the equation of the curve is (a) ( b ) (c) y=( d ) e^(( e ) (f) K(( g ) (h) x-1( i ))( j ))( k ) (l) (m) (b) ( n ) (o) y=( p ) e^(( q ) (r) K e (s))( t ) (u) (v) (c) ( d ) (e) y=( f ) e^(( g ) (h) K(( i ) (j) x-2( k ))( l ))( m ) (n) (o) (d) None of these

CENGAGE PUBLICATION-APPLICATION OF DERIVATIVES-All Questions
  1. The curve y=a x^3+b x^2+c x+5 touches the x-axis at P(-2,0) and cuts t...

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  2. If the function f:[0,4]->R is differentiable, the show that for a , b ...

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  3. The slope of the tangent to the curve y=sqrt(4-x^2) at the point where...

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  4. If at each point of the curve y=x^3-a x^2+x+1, the tangent is inclined...

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  5. If the line joining the points (0,3) and (5,-2) is a tangent to the c...

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  6. The curve given by x+y=e^(x y) has a tangent parallel to the y-axis at...

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  7. The number of tangents to the curve x^(3/2)+y^(3/2)=2a^(3/2),a >0, whi...

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  8. Show that the square roots of two successive natural numbers greater ...

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  9. If m is the slope of a tangent to the curve e^y=1+x^2, then (a)|m|>1 ...

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  10. The angle made by the tangent of the curve x = a (t + sint cost), y = ...

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  11. If f(x)=x^alphalogx and f(0)=0, then the value of alpha for which Ro...

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  12. The value of ′c′ in Lagrange's mean value theorem for f(x)=x(x−2)^2 in...

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  13. The point (s) on the curve y^3+3x^2=12y where line tangent is vertical...

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  14. The triangle formed by the tangent to the curve f(x)=x^2+bx-b at the ...

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  15. If the normal to the curve y=f(x) at the point (3,4) makes an angle (3...

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  16. The slope of the tangent to a curve y=f(x) at (x,f(x)) is 2x+1. If the...

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  17. Show that the normal at any point theta to the curve x=acostheta+at...

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  18. If a,b,c in R and a+b+c=0, then the quadratic equation 3ax^2+2bx+c=0 ...

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  19. The tangent to the curve y=e^x drawn at the point (c,e^c) intersects t...

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  20. Let S denote the set of all polynomials P(x) of degree lt=2 such tha...

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