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The no of roots of this equation are the no of points of intersection of y=x^4+x^3 and y=x^2+3kx+2k^2. Differentiating y=x^4+x^3 wrt x we get dy/dx=4x^3+3x^2=x^2(4x+3). dy/dx>0 when x> -3/4, dy/dx The...
Let us first calculate infinitesimal work done, dW by the force of gravity on the drop in the interval t to t+dt. Let’s assume the mass of the drop at time t be M(t) and its velocity at this instant...
Dear student, The general term of the series can be given by: So, the required sum can be found as: Using the standard formulae, the required sum can be found. Regards Sumit
If we need to know change of any quantity with respect to other, then we differentiate it. For example, we differentiate distance x with respect to time t to know how the distance is changed as time...
Ans: Hello Student, Please find answer to your question below You need to practice lots of questions in Application od derivative to acquire a confidence. Always try to find each and every question by...
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Ans: Hello Student, Please find answer to your question below Differentiation is a preocess of finding the derivative. Derivative is a fundamental tool of calculus. Thederivativeof afunction of a real...
The slope of the tangent at P(t) is dy/dx = dy/dt * dt/dx = t Let the tangent cuts the curve and normal at Q(t 1), then the coordinates of the point is (3t 1 2 , 2t 1 3 ) The the slope of the line...
tan -1 √1+sinx/1-sinsx = tan -1 √(cos 2 x/2 + sin 2 x/2 + 2*sinx/2*cosx/2)/(cos 2 x/2 + sin 2 x/2 – 2*sinx/2*cosx/2) =tan -1 √(cosx/2 + sinx/2) 2 /(cos x/2 – sin x/2) 2 = tan -1 (cosx/2 + sinx/2)/(cos...
Ans: x 2 - y 2 /8 if, F(xy) = x 2 – y 2 /8, then F( x + 2y, x – 2y) = ( x+2y) 2 – (x-2y) 2 /8 = 4*x*2y/8 = xy Hence ans is x 2 - y 2 /8
Ans: Hello Student, Please find answer to your question below First we need to check the domain of the function ….......(1) So the domain of f(x) is (1). Since it covers all the principle...
Ans: Hello Student, Please find answer to your question below n = 1 So it form an AP with a common difference of ½.
Ans: Hello Student, Please find answer to your question below It is 0/0 form. Apply L’Hospital
Ans: Hello Student, Please find answer to your question below Function will always attain maxima at x = zero. You can calculate the value of x from here......(1) Then put the value of x from (1) in...
Ans: Hello Student, Please find answer to your question below, So there is an atleast one root lie between 0 and 1. So there is only one root .3473 between 0 and 1.
Ans: Hello Student, Please find answer to your question below In place of y, we have x & vice – versa. Area of triangle ABC …..........(1) Area of rectangle: …...........(2)...
Ans: Hello Student, Please find answer to your question below, Arrangement is something like this, but in place of y, we have x & vice-versa. Area of rectangle: …..........(1) Area of...
Ans: Hello Student, Please find answer to your question Apply the chain rule
Ans: Hello Student, Please find answer to your question ….....(1) From (1)
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