11. For the differential equation = z(1- y) (a) Sketch a direction field on the axes below. Include tangent line slopes at each point with integer coordinates (and more if you like). 2 1- -2 1- +2 (b) Sketch (on your direction field) a solution curve that satisfies . y(-1) = 0

Q: 58. Find an equation for the tangent line to the graph of y = Vx? + 3x at the point (1, 2).

A: The given function is y=x2+3x. Compute first derivative as follows. dydx=ddxx2+3x=12x2+3x…

Q: What is the slope of the tangent line to the graph of the solution of y'= 7√y + 6x3 that passes…

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Q: ind the slope of the line that is tangent the curve sin(2x)+sin y=e*y – 1 at (0,0). our answer…

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Q: Find the mean value of y = x² - 7 over the range -2 < x < 2, and enter your answer as a decimal in…

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Q: The tangent line to y = f(x) at (9,-10) passes through the point (6,-5). Compute the following. a.)…

A: Given query is to find the value of function and derivative at x = 9.

Q: 1 Find an equation of the tangent to the curve f(x) = /x + 8 that has slope 4 %3D - OA. 1 y =7x-3 O…

A: Equation of the line in slope-point form is:        m = slope (x1, y1) = point on the line

Q: 25. From what you know about the graphs of functions (i) through (v), pick out the one that is its…

A: We have given (1) y=sinx  (ii) y=x   (iii) y=x   (iv) y=ex   (v) y=x2   The functions (1) y=sinx…

Q: L. Find the Indicated derivative. 1. y; given r'+y' =8

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Q: Let f (x) = (x³ –- 2x + 2)° Lans(1) = (x' – 2x + 2)' ma g(x) = 5" (x) and 8 (x) = f¯l (x). What is…

A: The slope of the curve g(x) at a point will be the derivative of the function, g'(x) at that point.

Q: 2. What is the equation of the tangent line to the curve y = x? - 2x +1 at point (3,4)? а. у3 2x — 2…

A: The equation of line is y-y1=mx-x1, where m is the slope of the curve.

Q: 8. Suppose your bank gives an interest rate of 5% that compounds annually. If you currently have Php…

A: The derivative of a function is given by the expression dydx. It gives the rate of change of the…

Q: Find an equation of the tangent line for the curve.15 y + (xy + 2) = 0 at the point (3,-1) 3x-7y 16…

A: equation of tangent line at point 3,-1 for graph or curve xy+23+y2=0

Q: Use implicit differentiation to find the equation of the line which is tangent to the curve 2xy +…

A: Given equation: 2xy+3x2-5x=4 We know that slope of tangent will be defined by dydx-1,2

Q: Soluing liner differentil equations dy +2xy=2X 3.

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Q: Oe. 0.5 20. If an equation of the tangent line to the curve y = f(x) at the point a = 2 is y = 4x -…

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Q: Find the equation of y, given the derivative and the indicated point on the curve. dy dx = 2x - 1 y…

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Q: The graph of the function f(x) = sin(x+ 8) is shown along with the points (– 8, f( – 8)) and (– 7,…

A: (1) f(x)=sin(x+8)f'(x)=cos(x+8)slope =f'(-8)=cos(0)=1equation of tangent at…

Q: Let f (x) = x³ – 2x + 1 and g (x) = f=1 (x). 3 What is the slope of the curve g(x) = f-l (x)at the…

A: Since you have asked multiple question, we will solve the first question for you as per our guide…