Use an appropriate local linear approximation to estimate the value of the given quantity. Round your answer to four decimal places, if required. cos 32' 2 i

Q: find the length of the indicated portion of thecurve.r(t) = (et cos t)i + (et sin t)j + etk, -ln 4…

A: Given, r(t)=etcosti+etsintj+etk length L=∫-ln40r'(t)dt            .......(1) now derivate given…

Q: Find the length of the curve using formula.  y= ln (cosx) bounded by 0 and pi/4

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

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Q: Find the eguation of the tangent Line to the CUrre y= Cos( Son)e) at the Point mith coordinates (T)…

A: Given curve is, y=cos(sin(x)) we have to find the equation of the tangent line at the point (π,1) of…

Q: = V4 cos" : – 1, y = 10 < x < 30

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Q: Eliminate the paranoter t from the follewing S r(1) = 4+ sin t lu(t) 3- cost

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Q: Find an equation of the tangent line and normal line to the curve at the given point for the…

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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: Cos 33°~ (give e Excct an wer, using Jt as needed

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Q: Given the linear approximation at a = 0, determine the smallest value of x such that the linear…

A: the linear approximation of f(x) at a is :…

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

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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: Find the length of the given curve: where -4 < t ≤1. r(t) = (-2t, 2 sin t, 2 cos t)

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Q: mm? Let f (x) = vx .Find the equation of the tangent line to f(x) at x = 30. Using the linear…

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Q: d'y Find for dr? y = cot(x) dy %3D dx?

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Q: a) cosh (x) tanh' (?) = sech'! (?) find the "(?) " %3D %3D b) ln () = ? --

A: We are given : cosh-1(x)=tanh-1?=sech-1(?) Let,   Now, cosh-1(x)=tanh-1t=sech-1(y) Taking…

Q: Use Euler’s method to approximate the indicated function value to 3 decimal places, using h =   0.1.

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

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Q: Find the lengths of the curves x = cos t, y = t + sin t, 0 … t … pi

A: Solution:Given   x= cos t,      y= t+sin t,   0≤t≤πFormula:Lenght=∫dxdx2+dydt2dt1+cos 2x=2 cos2…

Q: Find the lengths of the following curves: e. x = 8cos t + 8t sin t and y = 8 sin t – 8t cos t,…

A: Solution:Givenx=8 cost+ 8t sinty= 8 sint -8t cost,   0≤t≤π2To find the length Formulaarc…

Q: Find the extrema of the function below using Newton's Method. cos( ) +x² – 3r

A: Here we have to find the extrema of the function f(x)=cosx4+x2-3x using Newton's Method.…

Q: The velocity v and time t are related by the first order differentia pelow. Find the velocity att =…

A: Here we have,  dvdt-15vtant5=20 given v(0)=1. Where v= velocity,  t = time

Q: 3. Find the slope of the tangent line to r?ey + y²e² = 2e at (1,1). %3D

A: Let's find slope of given tangent line.

Q: Find the slo pe of the Para bola y=X at the Point PC2,4).write an equation for the tangent to the…

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Q: Use linear approximation, i.e. the tangent line, to approximate 3.6° as follows: Let f(x) = x°. The…

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Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: The given question is the application of integration and solved as shown in step2.

Q: Find the length of the curve y = ln (cos x), 0&lt;= x&lt;= pai/3

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Q: A military radar identified an unknown object flying above Andaman Sea. The Radar Intercept Officer…

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Q: Find the distance s covered by a point moving with linear velocity v for the given time t.   v = 10…

A: Given, Velocity v=10ft/sec and time t=5 sec Now we need to find distance s covered by a moving…

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

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Q: For the cardioid r  =1+ sin0 of Example 7, find the slope of the tangent line when  0=pi/ 3

A: Then plug this in the slope of the tangent formula

Q: Find the first order derivative for the following: cot(e(+M)y) sin(My²) + Vx4 + Mex %3D

A: We will find  ∂T/∂x,    ∂T/∂y

Q: Find the length of the curve y = ln (sin x),  pai/6&lt;=x&lt;=pai/2.

A: The given curve is,

Q: Given that y = In(4 + x²), %3D find dy (a) dx' (a) the equations of the tangent and normal to the…

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: To use the geometry we will change the polar equation into the cartesian equation first.  For that,…

Q: the wire that lies along the curve Di + (7 sin t)j. 0sts5 Osts1; 8= 5? its

A: We have to find the mass of wire according to the given information

Q: Given h(x) = ,(2t? – 4t) dt, write the equation of the tangent line at x = 1. %3D

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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Q: Find the first order derivative for the following: cot(e(3•Z)t) sin(z•t²) S = t5

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Q: The graph of y = 2x (x+ 1) and y = 1 (x>0) intersect at one point, x=r, as shown to the right. Use…

A: Let the given functions be, hx=2x2x+1gx=1x Equate both the functions,…

Q: Find the equation of the tangent to x = = VE , y = t – at the point where t = 4. Note: Sample format…

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Q: 10 cos 0 and y = 10 sin³ 0, find the total length of the curve swept out by the point If x = (x, y)…

A: We have to point length of curve swept out by the point:

Q: If y = tan u, u = v - and v = In x, what is the value of at x = e? dx sec?e 1 O Option 4 O Option 3…

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Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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Q: Consider the following. x = 3 cosh(t), y = 2 sinh(t) (a) Eliminate the parameter to find a Cartesian…

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

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Q: Find the tangent of ZH. J 4 H. 3-/6 Write your answer as an integer or as a decimal rounded to the…

A: Given triangle HJI

Q: Find the distance s covered by a point moving with linear velocity v for the given time t.   v = 20…

A: Velocity, distance, time: Velocity V=20 ft/sec Time t=4 sec.