Homework Answers
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + co...
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) -...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
Given the function y = 4 - 2 sec x + tan x Find the equation...
Given the function y = 4 - 2 sec x + tan x Find the equation of the tangent line to the curve at the point P(0,?).
Q3 (Show your work!) 25 Points Let • f(x) = a - (x + b), where...
Q3 (Show your work!) 25 Points Let • f(x) = a - (x + b), where a, b and care constants • the graph of y = f(x) has a vertical tangent line at its inflection point (1,2) the tangent line to the graph of y = f'(x) at x = 2 is perpendicular to the tangent line to the graph of y = e-sin at x = 0 Find the values of a, b and c and sketch the...
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal...
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y...
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
x2–2x-3 Let f(x) = Find the X-value(s) for which the graph of y = f(x) has...
x2–2x-3 Let f(x) = Find the X-value(s) for which the graph of y = f(x) has a horizontal tangent line. x+2
show work 9. tan 37 10. sec 4 11. Find sin(x + y) and cos(x +...
show work
9. tan 37 10. sec 4 11. Find sin(x + y) and cos(x + y) if cosx = - cosy = -— x is in quadrant II and y is in quadrant III. [10] 12. Find the exact value of sin 2x and cos 2x if sin x = and cos x = - [6] 5 13. Simplify tan (x + 3) to a form involving sinx, cosx, and/or tanx. [6]
5. Find the derivative of f(x) = ln (sec(x) + tan *' (x)). 6. Find an...
5. Find the derivative of f(x) = ln (sec(x) + tan *' (x)). 6. Find an equation of the tangent line to the curve y = x’ In(x) when x = e?
3. (16) Find the general solution of y"+y = sec (r) tan (x). For each part...
3. (16) Find the general solution of y"+y = sec (r) tan (x). For each part below, circle your final answer. Find y Let th= 12 W 12 W = 0 f (2) 0 W = = = y = General solution y =
1. Express the limit as a derivative and evaluate. 17 lim 16+h-2 lim 2. Calculate y. tan x 1 + cos x y sin(cos x) y= sec(1 +x2) x cos y + sin 2y xy Use an Implicit Differentiation] 3. Find y" if x, y,6-1. [Use Implicit Differentiation] 4. Find an equation of the tangent to the curve at the given point. 121 12+ 1 [Use Implicit Differentiation] 4. Find the points on the ellipse x2 + tangent line has...
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
Given the function y = 4 - 2 sec x + tan x Find the equation of the tangent line to the curve at the point P(0,?).
Q3 (Show your work!) 25 Points Let • f(x) = a - (x + b), where a, b and care constants • the graph of y = f(x) has a vertical tangent line at its inflection point (1,2) the tangent line to the graph of y = f'(x) at x = 2 is perpendicular to the tangent line to the graph of y = e-sin at x = 0 Find the values of a, b and c and sketch the...
f(1,y) = x² + 4xy + y2 – 2.c + 2y +1. f(x,y) has a horizontal tangent 1. Find all points (a,b,c) where the graph z = plane (parallel to the xy-plane). 0 has a horizontal 2. Find all points (a,b) where the level curve f(x,y) tangent line (parallel to the z-axis).
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
x2–2x-3 Let f(x) = Find the X-value(s) for which the graph of y = f(x) has a horizontal tangent line. x+2
show work
9. tan 37 10. sec 4 11. Find sin(x + y) and cos(x + y) if cosx = - cosy = -— x is in quadrant II and y is in quadrant III. [10] 12. Find the exact value of sin 2x and cos 2x if sin x = and cos x = - [6] 5 13. Simplify tan (x + 3) to a form involving sinx, cosx, and/or tanx. [6]
5. Find the derivative of f(x) = ln (sec(x) + tan *' (x)). 6. Find an equation of the tangent line to the curve y = x’ In(x) when x = e?
3. (16) Find the general solution of y"+y = sec (r) tan (x). For each part below, circle your final answer. Find y Let th= 12 W 12 W = 0 f (2) 0 W = = = y = General solution y =
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