1. Consider the curve eb = =2 + sin(5g). (a) Use implicit differen...

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1. Consider the curve eb = =2 + sin(5g). (a) Use implicit differentiation to find dy/dx. (b) Find the slope of the line tangent to the curve at the point (1,0). (c) Explain why there are no points on the curve where the tangent line is horizontal. (You can/should do this without trying to graph it.) 2. For a and b positive real numbers, consider the elliptical curve = (a) Find dx and SVW dx² y (in terms of x, y, a and b). (b) Now set a = 3 and b = 5. Find the equation for the line tangent to the curve at the point (2, 5.15). Where does this line meet the y-axis? 3 3. Logarithmic differentiation sometimes makes difficult problems easier; do the following two exercises to (hopefully) get a sense of this. In both parts, f and g are functions of x. (a) Use logarithinic differentiation to prove the product rule (b) Use logarithmic differentiation to prove the quotient rule #(6)- g² 4. Let f be an invertible function (with inverse f-1). Suppose that we know f is differen- tiable at every point of its domain. True or False: f- must be differentiable at every point of its domain. Justify your answer.

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