in the following problems. Write your solutions and fir answers on a separate sheet. Tangent and normal lines are drawn to the curve y = x at x = 2. 11. What is the equation of the line tangent to the curve at the given point? A. y = 12x - 16 B.y = x - 16 C. y = x- 12 D. y = 12x 12. What is the equation of the normal line drawn to the curve at the givenp Sinto C. y = x+49 x+8 А. у — 6.

Q: Find an equation for the line tangent to the graph of y=tan-1(x) at the point (1,π/4).

A: Given information:

Q: Find the equation of the line that is tangent to the curve y = 4x cos x at the point (T, -47). The…

A:

Q: Function Point h(t) sin t + et %D 7 7

A:

Q: At which of the following values of x does sin(4Ttx?) attain the largest slope? (a) x = 0 O (b) x =…

A:

Q: b. If B(x) = /g(x), what is the equation of the tangent line drawn to B(x) when x = 1? %3D

A: b) if B(x)=g(x)we have to find the equation of tangent line drawn to B(x) when x=1   differentiate…

Q: B. Solve the following problems: 1. Find the equation of the tangent line to the the curve y = 3x² –…

A:

Q: 1 The slope of the tangent line to the graph of y = at a = 1, is 3e². %3D e (r + 2) Select one: a.…

A: Given curve: Now,

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: A particle travels along the a-axis such that its velocity is given by v(t) = (t0.5 + 5t) sin (2t).…

A: To Find: Distance travelled by partical in interval 0 to 4

Q: Find the equation of the tangent line to the curve y = 5 sec(x) – 10 cos(x) at the point (T/3,5).…

A:

Q: he equation of this tangent line can be written in the form y = mx + b where ?= nd b =

A:

Q: If PQ and PR are tangent to O E in the given figure, find the value of x. 9x-40 E • 4x+5 Q

A: from a point length of the tangents on the are equal so  PR = QR

Q: 4.1. Find the slope of the line tangent to r = 4 – 3 sin 0 for 0 = ™

A: The given question is based on the tangent and normal topic in which we have to find only the…

Q: Answer the following: a.) What is the equation of the line tangent to the curve y=x^2 at x=1? b.)…

A:

Q: Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and…

A:

Q: Solve the following. Show the step-by-step solution. 1. Find the equation of the tangent line and…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: The given function is y=x2-4x and the point is 1,-3

Q: Find the equation of the tangent and normal to the following corce at the points indicated against…

A:

Q: r = -1 + cos 0 0=t/2

A: In the question we have to find the slope of function -…

Q: Find the equation of the tangent line to the curve y = 5 sec(x) – 10 cos(x) at the point (T/3, 5).…

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: Given the graph of r sin 2y = y cos 2x pictured at right, what is the point-slope equation for the…

A: The derivative of the function y'=dydx is the measure of how fast the function is changing with…

Q: In the given equation , find the slope of the tangent line to the graph at the given point :-…

A: Given the equation is  x2+4y=8. Point given on the graph is (2,1). To find the slope of the tangent…

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: 1 Find an equation for the line tangent to the graph of y=2 tan at the point (3,1/8).

A:

Q: The graph of the curve + y° = 6xy is shown above. The slope of the tangent line to this curve at the…

A:

Q: Question 12 Find the slope of the tangent line to y = at X = 1 3 - х

A: The given curve is y=23-x, x=1 Differentiate the curve with respect to x      dydx = ddx23-x       =…

Q: Find the equation of the tangent line to the curve y = 3 sec(x) – 6 cos(x) at the point (T/3, 3).…

A: Given : y =3secx - 6cos(x)

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

A:

Q: Complete the following sentence: The equation of the tangent line to the curve y=2/x+1 at x= is…

A:

Q: For what value(s) of t will the slope of a line tangent to x = 6 sin t, y = t² + t be undefined, for…

A: Here we have to find the slope of the tangent line.

Q: please help me with this

A:

Q: 2 + 7x = sin(ry²) + y dy Answer: dr Find the equation of the tangent line to the curve at the point…

A: Consider the curve and differentiate w.r.t. "x".

Q: At the given point, find the line that is normal to the curve at the given point. 6x <y - TT Cos y =…

A:

Q: Find the equation of the line tangent to the graph of y=tanx at the following values of x a) x=0…

A: y =tanxa dydx = sec2xx=0 = 1        (0,0) ∴ Equation of line tangent         (y-0) = 1(x-0)     y=x…

Q: Determine the line tangent to y = sin x that is parallel to 2x – 4y = 8.

A:

Q: find the equation of the line TANGENT of the given curve for x=pi/6 y=5cos(2x)

A: Explanation of the answer is as follows

Q: Which of the following is the equation of the curve that passes through (1,3) and having the slope…

A: We want to find true option.

Q: find (a) the slope of the curve at the given point P, and (b) an equation of the tangent line at P.…

A: a) find the slope of curve at point P(1,-3).Find the derivative of the following function.

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

A: Given, To get the equation of the tangent line, finding slope is the first step. Here both x and y…

Q: If y = -cos x, what x-value corresponds to a y-value of between T and 27? ? ]T

A:

Q: 2. 7(t) = at t = 0

A: according to our guidelines we can answer only three subparts, or question and rest can be reposted.…

Q: Find, correct to two decimal places, the coordinates of the point on the curve y =sin x that is…

A: Given that y=sinx So coordinate point is x, sinx.

Q: 2. Consider the curve given by 3y2 – 2x²y³ +2x +9 = 0. Write an equation for the tangent line to…

A: The given curve is, 3y2-2x2y3+2x+9=0 The slope of the tangent curve is given by dydx Determine the…

Q: At the given point, find the slope of the curve and the line that is tangent to the curve, as…

A: Given :2x2y-πcosy=3π(1,π)

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

A: We need to find an equation for the tangent line to the curve at a given point of t. Also, we need…

Q: If h(x) = 5 – 4x", find h' (2). Use this to find the equation of the tangent line to the curve y…

A:

Q: Given the curve y=x2 and a point (5,17) Find the x intercept of the tangent line to the curve…

A:

Q: Find the equation of the line tangent to the graph of y = sin r at the following values of x. NOTE:…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.