## Solving problems in differential calculus: I, Part 2 |

### From inside the book

Results 1-3 of 9

Page 3

Leslie Maurice Brown. has nothing to do with a proof, perhaps makes the result

look not unreasonable. (i) If any function F(n) always

then either F(ri) tends to a finite limit, or F(ri) tends to infinity, as n tends to infinity.

Leslie Maurice Brown. has nothing to do with a proof, perhaps makes the result

look not unreasonable. (i) If any function F(n) always

**increases**as n**increases**,then either F(ri) tends to a finite limit, or F(ri) tends to infinity, as n tends to infinity.

Page 11

Hence as a general description of the curve, as x

values, y decreases to a minimum at (0, 0); it then

4-69) and then decreases again, though never crossing the x-axis. It

consequently ...

Hence as a general description of the curve, as x

**increases**through negativevalues, y decreases to a minimum at (0, 0); it then

**increases**to a maximum at (4,4-69) and then decreases again, though never crossing the x-axis. It

consequently ...

Page 56

As y

- 1 to + 1 . It is convenient of modify the equation further eiogy_e-iogy ^ y-y'1 _ y2-

l x = tanh log y Thus elog3> + e-logj» y+y'1 y2 + l 2 l+X ll+X y - — , y = /• • l-x V ...

As y

**increases**from 0 to +oo, log y**increases**from — oo to + oo, x**increases**from- 1 to + 1 . It is convenient of modify the equation further eiogy_e-iogy ^ y-y'1 _ y2-

l x = tanh log y Thus elog3> + e-logj» y+y'1 y2 + l 2 l+X ll+X y - — , y = /• • l-x V ...

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Common terms and phrases

3cot 5cot absolutely convergent Additional Examples angle approximately Binomial series circle circular functions conditionally convergent constant convergent series cos2 cos3 cosec cosh x+sin cosh2 decimal places Deduce derivative DIFFERENTIAL CALCULUS dt dt dx2 dx dy/dx error exponential function feet Find the Maclaurin Find the stationary finite limit flex geometric series harmonic series Hence hyperbolic functions increases l+x2 Leibnitz's Theorem loga logarithm Maclaurin expansion Maclaurin's Series maximum minimum Multiply nt+a oscillates finitely polynomial positive integer positive terms power series power series expansion principal value prove radians radius of convergence sec2 sec3 sech sech x series diverges series is convergent series oscillates sin2 sin3 sine sinh x sinh2 sinx Sketch the graph stationary points tangent tanh tends to infinity term by term triangle ABC true for y2 ur(x x—sin x+cos