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Show that sinx - x + x^3/6 >=0 for x>0

The rise and fall of the tide approximate SHM. Suppose the interval between sucessive high tides in a certain harbour is 12 hours 30 minutes and that in the entrance the depth of water at high tide is 10m and at low tide is 6 m. If on a certain day low tide occurs at 6 am at what time will the...

The altitude of a right-angled triangle is 6 cm and the base is increasing at a constant rate of 2cm/s. At what rate it the hypotenuse increasing when its length is 10 cm? No idea how to do this question. But i did approach it. I tried using similar triangles but it didn't work out. Why...

Two Straight roads meet an an angle of 60 degrees. A starts from the intersection and travel along one road at 40km/h. One hour later B starts from the intersection and travels along the other road at 50km/h. At what rate is the distance between them changing three hours after A starts.

At the highest point of its path, a body has a velocity of 10 m/s and is 8m above the ground. Find the angle of projection and initial velocity.

On the related texts that we had to find, can both texts be talking about the same event? Or should we have two texts that talk about different events?

A straight railway track and a straight road intersect at right angles. At a given instant, a motor car at 40 km/h and a train at 50 km/h are moving away from the intersection and are 40 and 30 km respectively from the intersection. At what rate is the distance between them changing one hour...

An object falling in a vertical line passes a window 3 m high in 1/6 seconds. Find the distance above the top of the window from which the object let fall. No idea about this question at all.

Simple calculus question that i just cannot get my brain around currently. A lamp is 6m directly above a straight path. A man 2m tall walks along the path away from the light at a constant speed of 1 m/s. At what speed is the end of his shadow moving along the path? At what speed is the...

Remainder of P(x) = x^3-3x^2 + 4x -2 when divided by (x+i) Isnt P(-i) = -i + 3 -4i -2 since (-1 x i)^2 = 1 x i^2 = -1?

This integration is killing me: S 2x(4+x^2)dx = (4+x^2)2 but S 2x(4+x^2) dx = S 8x + 2x^3 = 4x^2 + x^4/2 Any help explaining?

Trig Rules dose not cover (pi/2 + theta) does it? Like cos (pi/2 + theta) = sin (theta)

Does the marks that separate each rank in the school affect your overall HSC result? For example, say if 1st and 2nd second rank, were differentiated by 1 mark internally, but by 10 marks externally, will 2nd rank drag down 1st rank?

2 Questions that are destroying me: 12. PQ is a focal chord of the parabola x^2=4ay. Perpendiculars PA, QB are drawn from P, Q to meet the directrix at A, B repsectively. Prove that PB, QA intersect at the vertext O

Use Induction to prove statement true for all positive integers n \frac{1}{n} \leq 1+ \frac{1}{2} + \frac{1}{3} + ... + \frac{1}{n} - ln\ n \leq 1 Hence show that e * e^{\frac{1}{2}}*e ^{\frac{1}{3}}...*e^{\frac{1}{n}} does not converge to a limit

For this proof, can i do it like this? \int_{0}^{a} f(x)dx = \int_{0}^{a} f(a-x)dx \text{Let u=a-x }, du = -dx , x=a \ u=0, x=0 \ u=a\\ \int_{0}^{a}f(a-x) = \int_{a}^{0}f(u) -du(\text{Swapping Limits })\\ =-\int_{a}^{0}f(u) \\ =\int_{0}^{a}f(u) du =\int_{0}^{a}f(x) dx ( \text{since u is dummy...

If they ask for the cartesian equn of an elipps, with x=3cost, y=2cost Would it be sufficent to say a=3, b=2 thus x^2/9 + y^2/4 = 1

Is it applicable? Since it saves alot of time.

How are they defined? I had ideas that they were undefined and hence were critical pts. But also, i saw in Patel, that relative maxima, relative minima, and inflexion pts are criticals. Expand anyone?

THe sum of the angles of a polygon of n sides is (2n-4) right angles, n>=3