5) a function f: R^n=>R is said to be even, if f(x)=f(-x) for all x?R^b. If f is differentiable and even, compute Df at the origin of R^n. 6) determine the equation of the line tangent to the path ( cos^2, 3t-t^3, t ) at t=0.7) calculate an equation for the plane tangent to the surface ( cos x)( cos y)e^z =0 at the point (pi/2 , 1, 0)8) for each of the following curves C parameterized by the indicated path C, find the tangent space TpC at the indicated point:a) c(t) = ( tcost, tsint), p= c(pi) b) c(t) = ( e^t , e^(2t)/ sqrt 2 , e^(3t)/3) at an arbitrary point p= c(t)

1) Consider the function f. 182-SIR defined by : if ( x , y ) # 10 , 0 ) 0 7 if ( x, y ) = 10 , 0 ) Is this function continuous at the point (20 ) ? If you, give a demonstration, If not, explain why 2) Consider the function ?: 10' IR defined by . Ixy |4 0 Hip ( x , 4 ) = 60 , 0 ) Is this function differentiable at the point ( 0, 0) ? If yes, give a demonstration , If not, explain why. Is it continuous at the point ( 9 0 ) ( why ? ) and gla, y ) - (ex, cos( y - x ) , ey ) at justify why fund , are differentiable DVor their respective domains . b ) - Compute D(fog) (Dio) using the chain rule. " ) show that the equation Ry + B + 3 xB = 4 can be solved for 2 as a function of ( x, y) in a neighborhood of the point (, 0, 1 ). Compute azlan and at lay at the point ( 1,0 )