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Β Reduce the following fraction into partial fractions:Β 3x^ 2 + 7x + 28/x(x^ 2 + x + 7)
Find the absolute extrema of the function on the indicated
interval
1. π(π‘) = 2 sec 1/2 π‘ ; [ β1/3π,1/2π ]
2. π(π₯) = π₯Β³ + 3π₯Β² β 9π₯ ; [β4, 4]
3. π(π₯) = π₯Β³ + 5π₯ β 4 ; [ β3, β1 ]
4. β(π₯) = (π₯ β 3)^1/3 + 4 ; [ 0, 2 ]
5. π(π‘) = 3 cos 2π‘ ; [ 1/6π,3/4π ]
Prove that the map F: R^2 to R^2 given by F(x,y)= ( e^x cosy, e^xsiny) is not invertible on the whole of R^2 , but is locally invertible at each point of R^2.
Find the domain of the following
f(x,y,z)= z/(x^2-y^2)
Given the function f, discuss its relative maximum and minimum
points, the intervals where it is increasing and decreasing, the intervals of concavity, and the points of inflection. Construct a sketch of the graph of the function.
1. π(π₯)= 2π₯β4 / xΒ²
2. π π₯ =10π₯ / 1+3π₯Β²
3. π π₯ = π₯Β³ β 3/2 π₯Β²
4. π π₯ = π₯ β π₯Β³ / 3
Find the laplace transform of sinat where a is a constant
Laplace transform of t2
integrate the following with respect to x up to a constant C:
- 5x4- 4x3 + 2x - 3
- 3sin x - 2cos x
- (x3 + x)cos 5x
- e2x + sin3x
An object is thrown vertically upward with an initial velocity of 75ft/sec from a building 40ft above the ground. (a = 32ft/secΒ²)
1. Determine the equation of the distance s from the ground at a given time t in seconds.
2. Calculate the distance of the object from the ground after 2 seconds.
Check the continuity of the function
f: R^2to R at(0,0) , where f is defined by
f(x,y) = { 3x^2y/( x^2+y^2) , if (x,y)β (0,0)
{ 3 , if (x,y)= (0,0)
