The linear approximation at x = 0 to sin(2x) is A + Bx where A is: and where B is:

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

A:

Q: Find an equation of the tangent line at the given point on the curve. (a) x = 2 – 3 cos 0, y = 3+ 2…

A:

Q: The linear approximation at r 0 to sin(2r) is A+ Br where A is: and where B is:

A:

Q: Given: tan-1(e0.13-0.8) Get the local linear approximation to estimate the value of the given

A: According to question given that tan-1e0.13-0.8

Q: Obtain the general solution using separation of variables. dz = a(cos 0 dz + z sin 0 d0) %3D

A: Separation of variables.

Q: Evaluate f(x) dx, where f(x) = 13 sin(x), 0< x < T. f(x) dx =

A: The solution is given as

Q: If sin(x) f(x)= 68+t2 dt Jtan(x) and g(y)= f(x) dx , Then g) is equal to

A:

Q: the linear approximation for f(x,y) = sqrt (y+cos^2 x) at (0,35) is ?

A:

Q: The velocity of a particle moving back and forth on a line isy = ds/dt = 6 sin 2t m/sec for all t.…

A:

Q: Give estimates, using linear approximation, for v9.2 and sin ( +0.02).

A: 9.2 Now let, fx=x,  x=9  &amp;  ∆x=0.2 Differentiating with respect to x, we get f'x=12x Now,…

Q: Let f(x)= 9 sin x/ 2 sin x + 4 cos x Then f'(x)= The equation of the tangent line to y=f(x) at a =…

A:

Q: Q: IF the value of (t) change from sin(“,) to cos( ",5. Find the dF for dx f(x, t) = V1+t³ Sa f(x,t)…

A: To find dFdx, whereF=∫αxβxfx,tdt, and fx,t=1+t3

Q: Let y = sin(2a). If Ax 0.1 at x = 0, use linear approximation to estimate Ay %3D Ay 2 = Find the…

A: In this question, concept of Linear Approximation is used. Linear Approximation The equation of a…

Q: бл Approximate sin by using a linear approximation with f(x) = sin x. 13 (等) z f(a) + f ' (a)·h = c,…

A:

Q: ().小) of af f(x, y)=sin 1+y, +cos %3D %3D X +1 s215 ||

A: To find The partial derivatives of f(x,y)

Q: The linear approximation at z = 0 to sin(4z) is A+ Bz where A is: and where B is:

A: Linear approximation is found by L(x)=f(x)+f'(x)(x-a) Differentiate L(x) with respect to x.…

Q: 1. If F(x)= = cos a sin r (√t-1)' dt, find F'(x).

A:

Q: B. Find y). 1. y = cosh?x 2. y = x tan-1 x - In vx2 + 1

A:

Q: If f(x,v) = ex In(5xy) find dy?

A: Given: fx,y=ex2ln5xy. To find: ∂2f∂y2 Solution: In partial derivative we differentiate with respect…

Q: The linear approximation at a = O to sin(7x) is A + Bx where A is: and where B is:

A:

Q: Find dw/ dt at the given value for the following functio 1) w=x² + y°, x = cos(1), y = sin(t), at †…

A: The given functions are w=x2+y2, x= cost  and  y=sint and t=π. Evaluate w in terms of t as follows.…

Q: Find the general antiderivative of the given function. f(x)= sin (7y)+ cos (3y)

A:

Q: Let y = = sin(3x). If Ax = 0.2 at x = 0, use linear approximation to estimate Ay %3D Ay 2 = Find the…

A:

Q: Find where y(x) is defined by d²y dr? (a) 3x2 – e2, (b) sin 3x + cos r, (c) 1+x – x2 + In r. - -

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: For the function f(x) = 2 sec (2x) tan (2x) + sin(x) + cos(x), find the most general antiderivative…

A:

Q: The equation of the tangent line to f(r) = at z = 1 is y = ar +b and the tangent point is (1, c).

A:

Q: Given f(x, y, z) = xe"y + sin(xyz), find fyzz

A: Derivatives of: Sin x is Cos x Cos x is -Sin x u

Q: 2- is the D.E:(3x² + y cosx )dx + ( sinx-4y )dy = 0 | a- - Exact b- linear D.E (show that)

A:

Q: Assuming 9x° – 5y - 4xy = 0 defines y as a differentiable function of x, use the theorem dx - to…

A: Given: 9x3-5y2-4xy=0 We have to calculate dydx(1,1) by the given formula.

Q: Find the linear approximation of f(x) = sin x, for x close to 0

A: The given function is: f(x)=sin x To find the linear approximation of it close to 0.

Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: Given that f(x) = sin a cos' r +2 (sin r + a)' +, the value of the constant and the least value of f…

A:

Q: Let y = sin(5x). If Ar = 0.4 at r = 0, use linear approximation to estimate Ay Ay 2 %3D Find the…

A:

Q: dy Given y³ In x + x¹e³y = sin-¹(xy), compute da

A:

Q: Using the substitution x = sec 0, dx S: J x2Vx2 _ 1 where x > 1, is equal to

A: We can find the answer as below.

Q: Find the value(s) of at y= 1 given that x2y+y2 = 5. dx

A:

Q: Find the most general antiderivative of f(x)=6e^x+5 sec^2(x), where -pi/2

A: Please see the answer below

Q: Given f(x,y) = ex cos y, Evaluate fy(2,0) O e² cos 2

A:

Q: Find an equation of the tangent llne to the về at the given poln 6x y = (x + 1)2' (0, 0)

A:

Q: Given f(x,y,z) = 7xyz where x = sin(2t), y = cos(2t) and z = -1t. Find df/dt at t = -1. %3D Give…

A:

Q: Find the value(s) of @ for which y = cos ot satisfies d'y + 16y = 0. di? Enter your answers in…

A:

Q: The linear approximation at I = 0 to sin(3r) is A + Br where A is: and where B is:

A:

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

A:

Q: use Euler's method to obtain an approximation to four decimal places of the indicated value by first…

A:

Q: 18. The equation of the tangent line to 2² sin T # 0 f(x) = 0 x = 0 at r = 0 is 1 (a) y = -x (b) y =…

A: Note:Since you have asked  multiple questions ,we will solve first question for you.To get remaining…

Q: Let f(x) = Vx. The equation of the tangent line to f(x) at = 1 can be written in the form y = mx + b…

A:

Q: Differentiate f(t) = (e + sin(2 – t))* %3D 29.

A: derivative of xn  = nxn-1 derivative of sinx = cosx derivative of ex= ex Derivative according to…