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Vector Functions
We very firstly saw vector functions back while we were looking at the Equation of Lines. In that section we talked about them as we wrote down the equation of a line in R3 in terms of a vector function (occasionally known as a vector-valued function). In this part we want to look a little closer at them and we as well want to look at some vector functions in R3 other than lines.
A vector function is a function which takes one or more variables and returns a vector. We will spend most of this section looking at vector functions of a single variable like most of the places in which vector functions come here will be vector functions of single variables. Though, we will in brief look at vector functions of two variables later.
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If 7sin 2 ?+3cos 2 ? = 4, show that tan? = 1/√3 . Ans: If 7 Sin 2 ? + 3 Cos 2 ? = 4 S.T. Tan? 1/√3 7 Sin 2 ? + 3 Cos 2 ? = 4 (Sin 2 ? + Cos 2 ?)
Integrate following. ∫ -2 2 4x 4 - x 2 + 1dx Solution In this case the integrand is even & the interval is accurate so, ∫ -2 2 4x 4 - x 2 + 1dx = 2∫ o
Definite integration It involve integration among specified limits, say a and b The integral is a definite integral whether the limits of integration are as: a and b
Here are four problems. Four children solved one problem each, as given below. Identify the strategies the children have used while solving them. a) 8 + 6 = 8 + 2 + 4 = 14 b)
Objectives After studying this unit, you should be able to explain how mathematics is useful in our daily lives; explain the way mathematical concepts grow; iden
If the distances from origin of the centres of 3 circles x 2 +y 2 +2alphaix= a 2 (i=1,2,3) are in G.P. , then length of the tangents drawn to them frm any point on the circles x2+
Prisoners Dilemma This is a type of non-zero sum game and derives its name from the given story: The district attorney has two bank robbers in separate cells and offers them
Find out if the following sets of functions are linearly dependent or independent. (a) f ( x ) = 9 cos ( 2 x ) g ( x ) = 2 cos2 ( x ) - 2 sin 2 ( x ) (b) f
What are square roots
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