![1. a) Find the slope and the equation of the tangent at x = y = 2 sin x + 4 cos x for the curve: [K-7 Marks] UVOM sanatos bas](http://img.homeworklib.com/questions/97652330-65d3-11eb-8315-299169271352.png?x-oss-process=image/resize,w_560)
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1. a) Find the slope and the equation of the...
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'()...
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
13) Find an equation of the tangent line to the curve y=sin(5x)+cos(8x) at the point (π/6,y(π/6)). what is the tangent l...
13) Find an equation of the tangent line to the curve y=sin(5x)+cos(8x) at the point (π/6,y(π/6)). what is the tangent line: 14) f(x)=4x^2cos(4x) what is the first and second derivatives and solve both for F(5) NOTE There should be four answers! 16) Suppose that f(x)=3x/(4−5x^)3 find an equation for the tangent line to the graph of f at x=2. the tangent line: y=
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...
se of thelr connection with secant lines, tangents, and instantaneous rates, limits of the form with Because o 12-E occur frequently in calculus. Evaluate this limit for the given value of x and...
se of thelr connection with secant lines, tangents, and instantaneous rates, limits of the form with Because o 12-E occur frequently in calculus. Evaluate this limit for the given value of x and function f. 31) fx)-5x2-5,x A) -15 31) BDoes not exist Differentiate the function and find the slope of the tangent line at the given value of the in -10 D) 5 32) s--44-53, t-1 A)-1 D) 1 C) 31 B)-31 Find the indicated derivative. 33) 33) Find...
Find an equation of the tangent to the curve at the point corresponding to the given...
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = cos(O) + sin(40) y = sin(0) + cos(40) O = 0 y(x) = Need Help? Read It Talk to a Tutor 2. [-14 Points] DETAILS SESSCALCET1 9.2.010. Consider the following: x = t3 - 12t y = 2 - 1 (a) Find the following. dy dr = dy dr2 = (b) For which values of t is the...
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given...
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
Question 2: Find for the following functions: (1) y=-42x2-3x -! 7x? -5x + 9 (3) y=...
Question 2: Find for the following functions: (1) y=-42x2-3x -! 7x? -5x + 9 (3) y= x+5 (5) Y= 7+3 (y = (3x* + 3x + 2)(x+1) (7) y =(5x + 7x) Page 1 of 2 Question 3: (0) Find the slope of the graph of y=f(x) = 3x - 6x +1 at the point (2,1) (ii) Find the equation of the tangent line to the curve y = f(x) = x*-10x2 + 9 at x=-1 (iii) Find the equation...
Find an equation in slope-intercept form of the line satisfying the specified conditions. Perpendicular to the...
Find an equation in slope-intercept form of the line satisfying the specified conditions. Perpendicular to the graph of 5x + y = -3 with y-intercept (0, 2) O y = 5x + 2 y = 1/3x + 2 O y = -5x + 2 O y = 1 / 3x + 2
Problem 3 (12 points) The curve with parametric equations (1 + 2 sin(9) cos(9), y-(1 + 2 sin(θ)) sin(0) is called a limacon and is shown in the figure below. -1 1. Find the point (x,y 2. Find the slo...
Problem 3 (12 points) The curve with parametric equations (1 + 2 sin(9) cos(9), y-(1 + 2 sin(θ)) sin(0) is called a limacon and is shown in the figure below. -1 1. Find the point (x,y 2. Find the slope of the line that is tangent to the graph at θ-π/2. 3. Find the slope of the line that is tangent to the graph at (,y)-(1,0) ) that corresponds to θ-π/2.
Problem 3 (12 points) The curve with parametric equations...
Question 1 1 pts Find the derivative of f(x) = cos(sin(3x)). Of"(x) --cos(3x) sin(sin(3x)) O f'() -- 3cos(3x) sin(sin(3x)) Of'(x) - 3cos(3x) sin(cos(3x]) f'x) --sin(3x) cos(cos(3x)) Question 2 1 pts Find the derivative of f(x) = cos(x^2 + 2x). Of "(x)=2x+2 sin(x^2 + 2x) O f'(x)= x^2 sin(x^2+2x) Of"(x)= (2x+ 2) sin(x^2 + 2x) f'(x)= -(x^2 + 2) sin(x^2 + 2x) O f'(x)--(2x + 2) sin(x^2 + 2x) Question 3 1 pts Use implicit differentiation to find the slope of...
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...
se of thelr connection with secant lines, tangents, and instantaneous rates, limits of the form with Because o 12-E occur frequently in calculus. Evaluate this limit for the given value of x and function f. 31) fx)-5x2-5,x A) -15 31) BDoes not exist Differentiate the function and find the slope of the tangent line at the given value of the in -10 D) 5 32) s--44-53, t-1 A)-1 D) 1 C) 31 B)-31 Find the indicated derivative. 33) 33) Find...
Find an equation of the tangent to the curve at the point corresponding to the given value of the parameter. x = cos(O) + sin(40) y = sin(0) + cos(40) O = 0 y(x) = Need Help? Read It Talk to a Tutor 2. [-14 Points] DETAILS SESSCALCET1 9.2.010. Consider the following: x = t3 - 12t y = 2 - 1 (a) Find the following. dy dr = dy dr2 = (b) For which values of t is the...
y = 3x0+ QUESTION 2 Solve the given differential equation. (The form of yp is given D2y + 25y = -5 sin 5x (Let y p = Ax sin 5x + Bx cos 5x.) sin 5x + c2 cos 5x + x sin 5x - 1 x cos 5x Oo oo cos 5x + = x cos 5x y = C1 sin 5x + C2 cos 5x + 5x sin 5x y = C1 sin 5x + C2 cos 5x...
EXAMPLE 2 Find sin$(7x) cos”7x) dx. SOLUTION We could convert cos?(7x) to 1 - sin?(7x), but we would be left with an expression in terms of sin(7x) with no extra cos(7x) factor. Instead, we separate a single sine factor and rewrite the remaining sin" (7x) factor in terms of cos(7x): sin'(7x) cos”(7x) = (sinº(7x))2 cos(7x) sin(7x) = (1 - Cos?(7x))2 cos?(7x) sin(7x). in (7x) cos?(7x) and ich is which? Substituting u = cos(7x), we have du = -sin (3x) X...
Question 2: Find for the following functions: (1) y=-42x2-3x -! 7x? -5x + 9 (3) y= x+5 (5) Y= 7+3 (y = (3x* + 3x + 2)(x+1) (7) y =(5x + 7x) Page 1 of 2 Question 3: (0) Find the slope of the graph of y=f(x) = 3x - 6x +1 at the point (2,1) (ii) Find the equation of the tangent line to the curve y = f(x) = x*-10x2 + 9 at x=-1 (iii) Find the equation...
Find an equation in slope-intercept form of the line satisfying the specified conditions. Perpendicular to the graph of 5x + y = -3 with y-intercept (0, 2) O y = 5x + 2 y = 1/3x + 2 O y = -5x + 2 O y = 1 / 3x + 2
Problem 3 (12 points) The curve with parametric equations (1 + 2 sin(9) cos(9), y-(1 + 2 sin(θ)) sin(0) is called a limacon and is shown in the figure below. -1 1. Find the point (x,y 2. Find the slope of the line that is tangent to the graph at θ-π/2. 3. Find the slope of the line that is tangent to the graph at (,y)-(1,0) ) that corresponds to θ-π/2.
Problem 3 (12 points) The curve with parametric equations...
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