math calculus

br Also , for x -1 , u -2 and for x 3 , u 38

Therefore

Also , for x 1 , u 4 and for x 2 , u 7

Therefore

Also , for x -1 , u -5 and for x 1 , u -1

Therefore Also , for x -8 , u 9 and for x -3 , u 4

Therefore

Also , for x 0 , u 1 and for x 1 , u 4

Therefore

12 . The required area A is definite integral of ydx from x -1 to x 1 (Because y is an even function or y

is symmetrical across y-axis

Therefore 13 . Given f (x x2-4 and g (x x 2

Upon solving the two , the point of intersection is x -2 and 3

Therefore , the required area is 14 . Given g (x 2x2-3x 1 g (x 0 for x ? and 1 and therefore , g (x 0 in (1 /2 , 1

15 . Fundamental Theorem of Calculus defines Integral as a Limit of Sum It can be written as a 0 , b 2 i .e . b-a 2

Therefore - 868 and a 0 , b 1 and n 5

Therefore , Left sum approximation gives And , Right sum approximation gives

We find that

Right Sum Approximation Actual Value Left Sum approximation

For n 5 Error is -15 .92 on Right Sum approximation and 9 .55 on Left Sum Approximation

and C (0 800 (in dollars ) is the cost function

Cost for producing 300 units per day will be

C (300 4100

Cost for producing 201st through 300th units per day will be

C (300 )-C (200 4100 - 3200 900

19 (a ) Given Demand function d (x 23 - 0 .05x and Supply function s (x 8 0 .000125x2 As -ve price has no physical meaning , therefore , the equilibrium point is x 200

At equilibrium point demand supply

Therefore (b ) Consumers ' surplus 0 and (c ) Supplier 's surplus 0

Right Hand Limit

Therefore , this limit does not exist , Hence (d

Hence (a

23 . Given , Cost function C (x 14x 1200 and Price Demand function br

(x 18

1 . Revenue function R (x 18x and

Profit function

(x R (x ) - C (x 4x - 1200

2 . Marginal Cost function MC (x C (x 14

Marginal Profit function MP (x

(x 4

Hence (a Therefore , slope of the tangent line at (7 , ln7 ) will be m 11 /7

Therefore , equation of the desired tangent line will be Therefore , all the options are wrong where C is the constant of integration

Hence (d

26 . The interval is incorrectly written as [8 ,4] , it should be [-8 ,4] as the left figure should be smaller than the right figure

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Hence (c...