Module 1: Solve the following problems: Solve the following problems: 1. lim x-+2x+1 x-1x2-2x-3 2. Find the vertical discontinuity of x+3 x-1 3. lim 3x+5 x-00 4x-3 4. lim sin3x X-0 X - 5. Find the derivative of the following. 3x-5 a. y = x+1 b. y = In (sin(3x-5)) C. y = e2x arc tan (2x + 3) d. 4x2 + 2xy + yz = 0 e. Find the partial derivative with respect to x of the function xy2 - 5y + 6 = 0.Application Problems 1. Find the slope of the curve x2+ y2 -6x -4y - 21 = 0 at (0, 7). Compute also the tangent line and normal line at (0,7) 2. Determine the radius of curvature at (1,2) of the curve y2 - 4x = 0. 3. The number of newspaper copies distributed is given by C = 50t2 - 200t + 10000, where t is in years. Find the minimum number of copies distributed from 2016 to 2021. 4. A boatman is at A, which is 4.5km from the nearest point B on a straight shore BM. He wishes to reach, in minimum time, a point C situated on the shore 9km from B, how far should he land if he can row at the rate of 6kph and walk at the rate of 7.5 kph. 5. A statue 3m high is standing on a base 4m high. If an observer's eye is 1.5m above the ground, how far should he stand from the base in order that the angle subtended is a maximum? 6. A Norman window is in the shape or a rectangle surmounted by a semi-circle. What is the ratio of the. width of the rectangle to the total height so that it will yield a window admitting the most light for a given perimeter? 7. The volume or the closed cylindrical tank is 11.3 cubic meter. If the total surface area is a minimum, what Is its base radius, in m? 8. The distance a body travels is a function of time and is given by x(t) = 16t + 8t2. Find its velocity at t = 3