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y=f(a^x) and f(sinx)=lnx find dy/dx Solution) dy/dx = (a^x)(lnx)f''(a^x), .........(1) but f(sinx) = lnx implies f(x) = ln(arcsinx) hence f''(x) = (1/arcsinx) (1/ ( ( 1-x
find the value of 0 that makes cos 21 degrees = sin 0 statement true.
The angle of elevation of the top of a tower standing on a horizontal plane from a point A is α .After walking a distance d towards the foot of the tower the angle of elevation is
One-to-one function: A function is called one-to-one if not any two values of x produce the same y. Mathematically specking, this is the same as saying, f ( x 1 ) ≠ f ( x 2
A body is constrained to move in a path y = 1+ x^2 and its motion is resisted by friction. The co-efficient of friction is 0.3. The body is acted on by a force F directed towards t
Rectilinear Distance (Total Travel Distance per Day Using Rectilinear Distance): It can be computed through using following formula: d(X, Pi) = |x - ai| + |y - bi| (Source: T
Solve discrete harmonic mapping of a given surface patch (suppose the surface is genus-0 and with one boundary) 1. Map the boundary loop onto a unit rectangle using chord-length
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Utilizes the definition of the limit to prove the given limit. Solution Let M > 0 be any number and we'll have to choose a δ > 0 so that, 1/ x 2 > M
Example: Find a general solution to the subsequent differential equation. 2 y′′ + 18 y + 6 tan (3t) Solution First, as the formula for variation of parameters needs coe
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