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Sketch the graph and find the area of the region that lies inside both
r = 1 and r = 2sinθ.
Shan, who is 2 meters tall, is approaching a post that holds a lamp 6 meters above the ground. If he is walking at a speed of 1:5 m/s, how fast is the end of his shadow moving (with respect to the lamp post) when he is 6 meters away from the base of the lamp post?
A woman standing on a cliff is watching a motorboat through a telescope as the boat approaches the shoreline directly below her. If the telescope is 25 meters above the water level and if the boat is approaching the cliff at 20 m/s, at what rate is the acute angle made by the telescope with the vertical changing when the boat is 250 meters from the shore?
with a full solution please and please include the given.
Find the common area enclosed by the following pairs of curves.
r^2=6cos2 theta and r=2cos theta
Check the local inevitability of the function f defined by f(x,y)=(x²-y²,2xy) at (1,-1). Find a domain for the function f in which f is invertible.
Using the Implicit Function Theorem, show that there exists a unique differentiable
function g in a neighbourhood of 1 such that g (1)= 2 and F(g( y), y) = 0 in a
neighbourhood of (1,2) where F(x,y) = x^5+y^5-16xy³-1=0.
defines the function F. Also find g′( y).
State a necessary condition for the functional dependence of two differentiable
functions f and g on an open subset D of .
R² Verify this theorem for the
functions f and g, defined by f(x,y)=(y-x)/(y+x) and g(x,y) =x/y
Find the mass of the solid bounded by z = 1 and
z = x² + y² the density function
being δ(x,y,z)=|x|
Find the third Taylor polynomial of the function f(x,y)= =1+5xy+3²y at (1,2)
Find angle between the tangents at t = 1 and t = 2 to the curve 𝑟̅ = 𝑡2 𝑖̅+ (𝑡3 − 2𝑡) 𝑗̅ + (3𝑡 − 4) 𝑘̅.
