dz 2 = -ry", where r = st“ and y = –st". Compute – as a function of s and t only evaluate this when s8 = -1, t = 1.

Q: Find the equation of the tangent line to the function f(x) = x3 + a2 – x – 3 at the point where x…

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Q: If the line y=x+4 is tangent to f(x)=ax2 +bx at the point (2,6), then a+b?

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Q: Find the equation of the tangent line to the curvey = √2-4 at the point (5, 1). Oy=2-1 Oy= 22-2 Ov=z…

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Q: Compute the indicated derivative. U(t) = 5.3t2 + 5.3; U′(4) U′(4) =

A: Given: U(t)=5.3t2+5.3 Finding the derivative of the given equation : ddtU(t)=5.3ddt(t2)+ddt(5.3)…

Q: Find the derivative of f at point P in the direction of u. f(1, у, 2) — Зг? + 8y? - 42?, Р — (9, 2,…

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Q: Calculate the derivative of the function. s (z) = () 8z+5 2z-6

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Q: Find the equation of the tangent line to f(x) = 2x* – 5xat x = 1. - Oy=3x+10 Oy=6x+19 Oy=6x-9 O…

A: Given equation: f(x)= 2x4- 5x f(1)= 2(1)4- 5(1)= -3

Q: Use the sign of the derivative to establish the inequaltiy In(1+x) > I -,V> 0. 2

A: See the attachment

Q: he tangent line to y = f(1) at (-3,9) passes through the point (9,-3). Compute the following.

A: The slope of the line passing through the points, (x1,y1) and (x2,y2) is given by .

Q: Find the equation for the line tangent to g(x) rcos(x) at x = 0

A: Given:The function g(x) = (x cos(x))/(x+2).Obtain the tangent line for the above function at x = 0.

Q: Find the slope of the tangent line to the function: 4y 27 1 + х2 At point (1, 1) . 2.

A: Given:

Q: Suppose the linear approximation for a function f(x) at a = 2 is given by the tangent line y = −2x +…

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Q: Determine the point on f(x)= 2x^e where the tangent is parallel to the line y= 2x-12

A: The equation of the curve is  f(x) = 2xe The line parallel to the tangent line on the graph of the…

Q: Find all the points on the curve x² y² + 2xy = 3 where the slope of the tangent is -1. O (1,1) O…

A: We have find possible point where the slope of the tangent is -1

Q: Find the equation of a tangent line to the curve y= 2x3 - 3x2 - 10x +1 which is perpendicular to the…

A: The equation of the line is      x+2y-6=0⇒y=-12x+3       in the form of line equation y=mx+c  So,…

Q: Find the equation of the tangent line to the function f(x) = -3x2 – 2x at the point where x form y =…

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Q: The equation of the line tangent to f(x) = (x² – 9) (2x – 1) at æ = 2 is y = 2x –*

A: Given that: f(x)=(x2-9)(2x-1)

Q: Find the derivative of f (z) = (2° – 5z) (2² + 6z – 6). a va la sin (a) f' (포) 3DD Please explain,…

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Q: is the equation af tangent line at X=/ y = mx+b. to the giaph of f c) =x² -x at x=/ m%= b.

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Q: .The line y + 2x = 0 is tangent to y = F(x). Determine F(x) if F(x) = 4x³ + 2.

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Q: The slope of the tangent line to the graph of the function y = 8VI - 4 at (16, 28) is O 1.50 O -1.75…

A: Given function is, y=8x-4

Q: 8y If the directional derivative of f(x,y)%D at (2,1) in the direction of (2a,-3) is equal to zero,…

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Q: calculate the derivative indicated r,(0), r(t) = (e2t, e−4t2, e6t)

A: It is given that, rt=e2t,e-4t2,e6t. Note that, If  rt=ft,gt,ht where f, g and h are differentiable…

Q: Find the derivative of the function f(x, y) = 2x² – y² at the point M = (1, 1) in the direction…

A: We have to find the derivative of the function fx,y=2x2-y2 at the point M=1,1 in the direction…

Q: Write the equation of the tangent line to f(x) = + In(a²) - 4 at x = 1. O y = 3x - 6 Oy = 4x - 7 Oy…

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Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 9 and f'(2) = 3. |3D

A: GIVEN FOR A FUNCTION f(x) ,f(2) = 9            &  f'(2)=3

Q: Find the equation of tangent and normal line for the following: f(x)=2x2-7 , (2,1) Sol. y=8x-15 ,…

A: Since you have posted a question with multiple sub-parts, according to our guidelines we will solve…

Q: Calculate the derivative of 2t – 1 > t + 2 r(t) =< 3t – 5, 2t2 + 5t + 7,

A:

Q: find the derivative of (2³ + j)² O 23 +j O 223 + j O 625 + j6z² O 325 + j3z?

A: Derivative of (z3+j)2 is 2(z3+j)2-1(3z2+0) = 2(z3+j)×3z2 = 6z2(z3+j) = 6z5+j6z2

Q: Given: /(x, y) = 3x² – 2y² at (-÷.0) in the direction from P (–.0) to Q(0,1). What is the…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Find the slope of the line tangent to the x³ – 2x + 1 at x = 2 curve y %3D %3D O-10 O 1/10 O-1/10 O…

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Q: Find the point(s) (x, y) on the function f (x) = V1+ 2x where the tangent line is parallel to the…

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Q: Find the slope of the tangent to the curve r+ 2xy + y = 16 at (1, 3). The slope is VEnter undof if…

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Q: 2) Find the equation of the tangent to f(z) = 3re² when x = 1

A: A detailed solution is given below.

Q: Find the linear approximation of the function f(x) = Vr + 15 at a = 1 and use it approximate the…

A: Given, f(x)= (x+15)1/4 a=1

Q: The point on the graph of f(x) = 1 where the tangent line is parallel to the line 3z + y = 1 is: %3D

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Q: The value of b makes the liney = 2x + b be tangent to the function f (x) = x² is

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Q: Evaluate the derivative So (3t² – 2t +1) dt. -

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Q: Find the derivative: y = (3x² – 2x) Væ5 – 2x + 2 27 –14a5 –30z² +36x –8 2y5 -2x+2 dy %3D dæ 27+15* –…

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Q: Find the equation of the line tangent to the function f(x) = (x – 1)3 + 2 at x = 1. O y = 2 O y – 2…

A: Given query is to find the equation of the tangent at x = 1.

Q: Find an equation of the line tangent to the level curve of the function x 3xy passing through the…

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Q: Find the slope of the line tangent to y = 3x(cos x) at (7/2, 7/2). A) -3/2 B) 3x/2 C) /2 D) -x/2

A: Consider the function  y=3x(cosx) Point : π2,π2

Q: #4. Find the equations of the tangent lines to the relation 3y = x² - 4y when x 2.

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Q: Find the equation of the tangent line to f(x) =3cscx+xsinx at X= 2 A y=x- 3 y=x+3+ 2 y=x+3 y=x+3-

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Q: The slope of the tangent line to the graph of the function y = 8vT- 4 at (16, 28) is O 1.00 O -2.25…

A:

Q: Find the equation of the tangent line to the function f(x) = r + 3z++4 at the point where x =-2.…

A: Given : fx = x3+3x2+x+4

Q: Compute the indicated derivative. U(t) = 5.9t2 + 5.9; U'(4)

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Q: Calculate the derivative using the appropriate rule or combination of rules. 22 + 2z – 8 z2+ z – 2…

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.