Example:
Solve the differential equation , ..
Solve the differential equation , ..Proof:
1 = A(x + a) + B (x - a) ..
1 = A(x + a) + B (x - a) ..Proof:
Put a + b - x = t -dx = dt when x = a, t = b x = b, t = a = LHS Put a - x = t -dx = dt When x = 0, t = a x = a, t = 0 ..
Put a + b - x = t -dx = dt when x = a, t = b x = b, t = a = LHS Put a - x = t -dx = dt When x = 0, t = a x = a, t = 0 ..Examples:
Derivatives are also used to trace the graphs of different functions. To optimise the value of a differentiable function of practical use, derivatives of the functions are applied. This chapter reveals with many more application of derivatives such as determining the relative error in me..
Application of Derivatives Introduction
Introduction - Let us began this chapter with the following statement: Often a physician may want to test how small changes in dosage can affect the body's response to a particular drug. An economist may want to study how investment changes with variation in interest rates. How the veloci..
Application of Derivatives Animation
Application of Derivatives Animation..
Application of Derivatives Animation..Theorem 1:
Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We shall prove the theore..
Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We shall prove the theore..Velocity-Time Relations using Calculus
Velocity-Time Relations using Calculus - The velocity-time relationship which has been derived graphically earlier, can also be obtained with the help of calculus. Acceleration is the rate of change of velocity, and therefore, can be expressed as Integrating both sides of the ab..
Velocity-Time Relations using Calculus - The velocity-time relationship which has been derived graphically earlier, can also be obtained with the help of calculus. Acceleration is the rate of change of velocity, and therefore, can be expressed as Integrating both sides of the ab..Position-time relation by method of calculus
Starting with the definition of velocity, However, v (t) = v (0) + at dx = v (0) dt + at dt Integrating the above equation and applying the following limits, i.e., at t =0, x (t) = x (0), after an elapsed time t, the displacement is x (t), we hav..
Starting with the definition of velocity, However, v (t) = v (0) + at dx = v (0) dt + at dt Integrating the above equation and applying the following limits, i.e., at t =0, x (t) = x (0), after an elapsed time t, the displacement is x (t), we hav..Pressure
The pressure exerted in figure (a) above = 1666.7 N m - 2 = 1666.7 Pa The pressure exerted in figure (b) above = 1000 ..
The pressure exerted in figure (a) above = 1666.7 N m - 2 = 1666.7 Pa The pressure exerted in figure (b) above = 1000 ..See what our Users say :
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