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Smooth Curve - Three Dimensional Space
A smooth curve is a curve for which →r' (t) is continuous and →r' (t) ≠ 0 for any t except probably at the endpoints. A helix is a smooth curve, for instance.
At last, there is requirement of discuss integrals of vector functions. By using both limits and derivatives like a guide it shouldn't be too surprising that we as well comprise the following for integration for indefinite integrals
∫ r→ (t) = {∫ f (t)dt, ∫g (t)dt, ∫ h(t) dt} + c→
∫ r→ (t) = ∫ f (t)dt i→ + ∫g (t)dt j→ + ∫ h(t) dt} k→ + c→
and the following for definite integrals.
∫ba r→ (t) dt = {∫ba f (t) dt, ∫ba g (t) dt, ∫ba h(t) dt}
∫ba r→ (t) dt = ∫ba f (t) dt i→ + ∫ba g (t) dt j→ + ∫ba h(t) dt k→
Along with the indefinite integrals we put in a constant of integration to ensure that it was clear that the constant in this case requires being a vector in place of a regular constant.
Find the least number that is divisible by all numbers between 1 and 10 (both inclusive). Ans: The required number is the LCM of 1,2,3,4,5,6,7,8,9,10 ∴ LCM = 2 × 2
Sally gets paid x dollars per hour for a 40-hour work week and y dollars for every hour she works over 40 hours. How much did Sally earn if she worked 48 hours? Since she worke
Types of distribution Population distribution This refers to the distribution of the individual values of population. This mean it is denoted by 'µ' Sample distributi
Find the solution to the subsequent IVP. ty' - 2y = t 5 sin(2t) - t 3 + 4t 4 , y (π) = 3/2 π 4 Solution : First, divide by t to find the differential equation in the accu
A police academy is training 14 new recruits. Some are working dogs and others are police officers. There are 38 legs in all. How many of each type of recruits are there?
my math skills are keeping me from getting my ged need help in all areas
a research on area of plane figures
Ravi is a teacher of Class 4 in a municipal school in Delhi. When the new school year started, he opened the textbook and started teaching the children how to write 4-digit numbers
Explain Angle Theorems ? Certain angles and angle pairs have special characteristics: Vertical angles are opposite angles formed by the intersection of two lines. Vertical ang
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
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