What angle does the tangent to the curve y(x) = sin² (x/9) + 13sin(x/9) at x = 9n make with the x-axis? %3D Express your answer to 3 significant figures. Choose the smaller angle, i.e., your answer should be positive and less than 90 degrees.

Q: 5. Determine the equation of the tangent line to (a) r= 2 sin e at = (b) r =1+ cos 0 at 8 =

A:

Q: -sinh(x) at x = 0 is dx21 Answer:

A: Derivative of the function

Q: O Find the equation of the line tangent to the curve at the given value of the parameter. x cost+…

A:

Q: For what value of t will the slope of a line tangent to x = 6 sin t, y = t² + t be 0?

A: We have to find t

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t 15)…

A:

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: We have given parametric equation x=4sint, y=2cost  We have to find the tangent line of the given…

Q: The exact value of the slope of the tangent line to the graph of the curve r = 9 + 8 cos(e), at e =…

A:

Q: can any thing said about the tengent to the curves y=sinmx and y= - sin(x/m) at the origion (ma…

A: Solution  Given

Q: Consider the equation f(x) = x* + 2x – e* – 3, approximate the root with accuracy up to 2…

A:

Q: A particle is moving in such a way that its velocity v is given by the equation v(t) = cost + sin t.…

A: Given : vt = cost + sint

Q: Find the length of the curve y=ln(sec(x)), 0≤x≤π/4.

A: please see the explanation below

Q: • What restriction (on x or y) does dy have? What dx point (x, y) does this correspond to? • Find…

A: According to our policies we are allowed to answer only one question at a time. If you want solution…

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

A:

Q: find the most general antiderivative or indefiniteintegral. You may need to try a solution and then…

A: we have to find the most general antiderivative of the given integral and then we have to verify the…

Q: 5. Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: The given parametric equations are, x=t3+cosπt, y=4t+sin2t+6. Find the equation of the tangent to…

Q: Eliminate the parameter f) from the following X(+)= -sint yl)= cost

A:

Q: Find the length of the curve y = ln(sec(x)), where 0 is less than or equal to x which is less than…

A:

Q: The exact value of the slope of the tangent line to the graph of the curve r = 5 + 4 cos(0), at e =…

A:

Q: Can anything be said about the tangent lines to the curves y = sin mx and y = -sin (x/m) at the…

A: slope of the tangent at the point of taattngency = slope of the curve at the point of tangency =…

Q: Find the derivative. sin t du 4-u? di cost OA. 4- sin?1 O B. cos t(4- sin ?1) OC. 4- sint - cost O…

A: We need to find the integration of given expression.

Q: Find by implicit differentiation. 2+ 4.x = sin(ry²) dy Answer: dx

A: the given implicit function is: 2+4x=sinxy2

Q: 3. Find the slope of the tangent line to the curve y = +2 x*+4x+7 4. Determine and 4 of y = (5.x² –…

A:

Q: dy if 6 + sin 2y = dx 2y + 3x by using implicit differentiation. 2y + 3x Find Hence, find the…

A:

Q: Find the lengths of the curves x = ln (sec t + tan t) - sin ty = cos t, 0 ≤ t ≤ π/3

A:

Q: Two particles start at the origin and move along the x-axis. For, 0 <t< 10 their respective position…

A: Given, x1=sint , x2=e-2t-1 ,0≤t≤10 To find the velocity, Differentiate with respect to t we get,…

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Tangent line for a curve at a point is a line which just touches it and is "parallel" to the curve…

Q: Q4: Find an equation for the line tangent to the curve 2y cos x = 4x sin y , at the point where x =…

A:

Q: 1. The Average Rate of Change ("ARC") to. Given that f(x) = -2x² +4, what is the ARC: 1) From 0 to 2…

A: Authoring guidelines: As per the authoring guidelines, we can solve only the first question. Please…

Q: The slope of the tangent line to the curve at (x,y) point is defined by (1+ k) e2a+e .If the curve…

A:

Q: The displacement of a particle moving back and forth along a straight line is given by the following…

A: The displacement of a particle moving back and forth along a straight line is given by the following…

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

A:

Q: for the equation dx ecosh-(x) = In(x) sinh-(y) Find %3D

A: Using differentiation of   product rule and implicit differentiation,

Q: Find dy/dx of y=1/ (tan-1 x)

A: The given function is: y=1tan-1x

Q: 1.) The slope of the tangent line to the wve y?= 5+-1 at PCi,e) 2.) Find the First denivative of…

A: Using derivatives.

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The height of an arch above the ground is given by the function y = 11 sin x for 0sxSr. What is the…

A: This question can be solved by applying the formula of average height of an arch.

Q: Find an equation of the tangent line to the curve at the point corresponding to the given value of…

A:

Q: Q2- Find for the following function :- dx 1- y = sinh-(tan x) – tanh-1(sin x)

A: We will differentiate using direct formula and chain rule.

Q: Use the composite trapezoidal and Simpson's rules with step length h = 0.4 to estimate In(2+3/x)…

A:

Q: Q2\A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Given that,

Q: ind the second derivative (y") of the following function step-by-step and simplify the nal results:…

A:

Q: What is the second derivative of the function y = -6 sin x cos x where x is? Round your answer to…

A:

Q: a) Differentiate implicitly to find for the equation x cos y = x2 y2 +1 dx %3D b) Find the equation…

A:

Q: Find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: Given,         x=t-sint , y=1-3cost , t=π3

Q: Use an appropriate local linear approximation to estimate the value of the given quantity. Round…

A: cos32° It can be written as, cos32°=cos30°+2° Now, fx=cosx, x=30° &amp; ∆x=2°=2π180 radians Now…

Q: The exact value of the slope of the tangent line to the graph of the curve r = 7 + 8 cos(0), at e =…

A:

Q: find all possible functions with the givenderivative. y' = sin 2t + cost/2

A: we have to find all possible functions with the given derivative y'=sin2t+cost2. the given…

Q: Find the length of the curve y = ln (sin x), π/6 ≤ x ≤ π/2

A: Given y = ln (sin x), π6≤x≤π2

Q: At what value of x does the curve 1„2 sin y = 3y +x² + 4x have a horizontal tangent? (Supporting…

A: