Higher Engineering Mathematics, Sixth Edition
302 Higher Engineering Mathematics Problem 6. Supplies are dropped from a helicoptor and the distance fallen in a time tseconds ...
Some applications of differentiation 303 Now try the following exercise Exercise 121 Further problemson velocity and acceleratio ...
304 Higher Engineering Mathematics It is possible to have a turning point, the gradient on either side of which is the same. Suc ...
Some applications of differentiation 305 (a) Considering the point (1, 3): Ifxis slightly less than 1, say 0.9, then dy dx = 3 ( ...
306 Higher Engineering Mathematics Hence (−2, 9) is a maximum point. Whenx=3, d^2 y dx^2 = 2 ( 3 )− 1 = 5 , which is positive. H ...
Some applications of differentiation 307 Now try the following exercise Exercise 122 Further problems on turning points In Probl ...
308 Higher Engineering Mathematics upwards to form an open box. Determine the maximum possible volume of the box. The squares to ...
Some applications of differentiation 309 Hence for the least surface area, a cylinder of vol- ume 200cm^3 has a radius of 3.169c ...
310 Higher Engineering Mathematics h O PQ r h 2 R^5 12 cm Figure 28.11 Volume of cylinder, V=πr^2 h (1) Using the right-angled t ...
Some applications of differentiation 311 The power developed in a resistorRby a battery of emfEand internal resistanceris given ...
312 Higher Engineering Mathematics Problem 22. Find the equation of the normal to the curvey=x^2 −x−2 at the point (1,−2). m=1 f ...
Some applications of differentiation 313 Problem 24. Giveny= 4 x^2 −x, determine the approximate change inyifxchanges from 1 to ...
314 Higher Engineering Mathematics The pressurepand volumevof a mass of gas are related by the equationpv=50. If the pres- sure ...
Chapter 29 Differentiation of parametric equations 29.1 Introduction to parametric equations Certain mathematical functions can ...
316 Higher Engineering Mathematics (a) Ellipse (b) Parabola (c) Hyperbola (d) Rectangular hyperbola (e) Cardioid (f) Astroid (g) ...
Differentiation of parametric equations 317 Determine the equation of the tangent drawn to the parabolax= 2 t^2 ,y= 4 tat the po ...
318 Higher Engineering Mathematics 29.4 Further worked problems on differentiation of parametric equations Problem 5. The equati ...
Differentiation of parametric equations 319 x= 3 t^2 ,hence dx dt = 6 t y= 6 t, hence dy dt = 6 From equation (1), dy dx = dy dt ...
Chapter 30 Differentiation of implicit functions 30.1 Implicit functions When an equation can be written in the formy=f(x) it is ...
Differentiation of implicit functions 321 du dx = du dy × dy dx = d dy (4ln5y)× dy dx = 4 y dy dx (b) Letu= 1 5 e^3 θ−^2 , then, ...
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