Calculus Answers

sketch the region of integration and write an equivalent double integral with order of integration reversed and then calculate it.

integral 0 to 3 integral 1 to e^y (x+y) dx dy

Differentiate the following function
g(x) = e
−5x +

1
x
− tan x
3 p
x
2 + 1 
.

Let f(x) = π −
√
7x − 9. Use the definition of the derivative to find f
0
(x).

Let f(x) = |2x − 10| + 2 .
a) Show that f is continuous at x = 5.
b) Show that f is not differentiable at x = 5.

Let f(x) = x^2
2 + 6x. Use the definition (ε − δ method) to show that
lim
x→−3
f(x) = −9 .

1) Let f(x) = π − √7x − 9. Use the definition of the derivative to find f′(x).
2) Differentiate the following function
g(x)=e^-5x + (1/x −tanx)^3 (√x^2 +1)

1) Differentiate the following function
g(x) = e^-5x + ((1/x)- tanx)^3 ( squat root of x^2 +1)

2)
Let f(x)= pi- squat root of 7x-9. Use the definition of the derivative to find f’(x)

Abdullah saves $600 for new car. Currently Abdullahhave $(n+1). If his per week saving is $(n). How long he waits to save at least $700 to cover his tax’s.Also, Give the geometrical representation of solution. Where n is your arid number (for example if your arid number is 19-arid-1234 then choose n=1234). (2 points)

Use Numerical Method to find Limit of function h(u)=bu^α,where b=2.01,α=0.25. Find lim┬(u→n)⁡〖h(u).〗Where n is your arid number (for example if your arid number is 19-arid-1234 then choose n=1234). Choose at least 4 nearest values of n for u from both sides (Do not choose far values from n marks will be deducted in that case). Perform all calculations then construct table and draw neat graph. And check whether the limit exist or not? If yes, then what is the value of limit. (4 points)

f(x)=2x^4+x^3-3x+2, then f ''(x)=
a)31
b)21
c)20
d)30