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Tangent Lines : The first problem which we're going to study is the tangent line problem. Before getting into this problem probably it would be best to define a tangent line.
A tangent line to the function f(x) at the instance x = a is a line which just touches the graph of the function at the point in question & is "parallel" (in some way) to the graph at that point. Consider the graph below.
In this graph the line is a tangent line at the specified point because just it touches the graph at that point and is also "parallel" to the graph at that point. Similarly, at the second point illustrated, the line does just touch the graph at that point, hence it is not "parallel" to the graph at that point & hence it's not a tangent line to the graph at that point.
At the second point illustrated (the point where the line isn't a tangent line) we will sometimes call the line a secant line.
Now, we've used the word parallel a couple of times and we have to probably be a little careful with it. Generally we will think of a line & a graph as being parallel at a point if they are both moving in the same direction at that point. So, in the first point above the graph and the line are moving in the same direction and so we will say they are parallel at that point. At the second point, on the other hand, the line and the graph are not moving in the same direction and so they aren't parallel at that point.
For the initial value problem y' + 2y = 2 - e -4t , y(0) = 1 By using Euler's Method along with a step size of h = 0.1 to get approximate values of the solution at t = 0.1, 0
Prove that sec 2 θ+cosec 2 θ can never be less than 2. Ans: S.T Sec 2 θ + Cosec 2 θ can never be less than 2. If possible let it be less than 2. 1 + Tan 2 θ + 1 + Cot
Find the normalized differential equation which has {x, xex} as its fundamental set
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1. Which of the following is greater than 4.3 x 10^9 a. 2.1 x 10^9 b. 3.2 x 10^9 c. 5.3 x 10^9 d. 7.4 x 10^8 2. Which of the following is less than 6.5 x 10^-5 a. 1.4 x 10
calculate the vector LM given l(4,3),m(-1,2)
probability as that of flipping a coin eight times and getting all the times the same side of the coin.)
What is minimum spanning tree? Determine a railway network of minimal cost for the cities in the following graph using Kruskal's algorithm. Ans: Minimum spanning tree in a con
Solve 3 + 2 ln ( x /7+3 ) = -4 . Solution This initial step in this problem is to get the logarithm by itself on one side of the equation along with a coefficient of 1.
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