Find the linear approximation of f(x)=lnx at x=1and use it to estimate ln⁡(1.3) L(x)=? ln 1.3≈?

Q: Suppose f(r) is a function whose Derivative f'(x) is graphed below on the domain [0, 9). y = f'(x) 1…

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Q: Find an equation of the plane satisfying the given conditions.

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Q: A particle is moving along the x-axis. The position of the particle at time t is given by x(t) = t3…

A: We have to use given formula to solve the problem

Q: Express the limit as a definite integral on the given interval. lim > x; In(2 + x;2) Ax, [2, 5] n-…

A: The solution is given below

Q: Use the Left Endpoint approximation method to approximate the area under the graph of the function…

A: This is a problem related to reimann left hand sum calculation. Based on the general formula we will…

Q: S sin x In(cosx) dx

A: To evaluate the integral: I=∫sin x(ln (cos x)) dx Substitute  cos x=t⇒-sin x dx=dt⇒sin x dx=-dt

Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

A: Given problem:- Use Lagrange multipliers to find the maximum and minimum values of f subject to the…

Q: endicular to the plane z + 3y – x = 7 and containing the points (2, 5, 0) and (0, 2, -1)

A: Here we have to find the equation of plane which is perpendicular to the other plane.

Q: Evaluate the definite integral. Use a graphing utility to verify your result. |2x - 9| dx

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Q: Solve the initial value problem below using the method of Laplace transforms. y" + 9y = 18t - 18t…

A: Let's find.

Q: Fin d: ) (3x*arctan x do Evaluate: s.) dx

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Q: Find the vectors that satisfy the stated conditions. NOTE: Enter the ezact answers using the…

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Q: xp sin 5x cos 3xt cos 5xsin 3x xp x²+ 2x + 5 EX Find:

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Q: 1) Find an equation of the tangent line to the curve y5+x2y3 = 1+x4y at the point (1,1).

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: Use the fact that the volume of a tetrahedron with adjacent edges given 1 au. (v x w)| to determine…

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Q: sin r da 4.

A: I am attaching image so that you understand each and every step.

Q: Snowy's Snow Cones has a special bubble gum snow cone on sale. The cone is a regular snow cone that…

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Q: * sin" (3y) cos" (3y) dy 10 (3y) dy COS 15360 111546435 256 156009

A: Given:   Given:    ∫0π6sin133ycos103y dy

Q: 1 (5* )csch- if y= (e oshS ) In Vx² +1 2 a) Find dx dy x+1 x>0. 2 x++1

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Q: Use the chain rule to find dy/dx for th following (a) y= (3x^2 - 13)^3

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Q: Find the directional derivative of the function at P in the direction of v. h(x, y, z) = xyz, P(8,…

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Q: Find unit vectors that satisfy the stated conditions. NOTE: Enter the exact answers in terms of i,j…

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Q: Evaluate the indefinite integral. x° (x® + 1)1/2 dæ Integral = INOTE: Remember to enter all…

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Q: Solve the following differential equations using the method of undetermined coefficients. y" – 2y" +…

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Q: Find an equation of the plane that passes through the points (2, 4, 1), (2,2, –4), and (-–3,5, 3).…

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Q: Find the exact length of the polar curve r = 2+2 cos 0 . Show All Your Work!

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Q: y" 2y'+ 17y-0; e cos(4x), e sin(4x), (-m, on). Venify that the given functions form a fundamental…

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. (2* + 9) dx

A: We need to find integral.

Q: 8. Ssin(1 – Int)dt

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Q: Find parametric equations of the line that satisfies the stated conditions. The line through (-8,-6)…

A: Let's find.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 6t, y = 8 -…

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Q: Match the answers to its antiderivative. Antiderivative Answer A. J kda In(z) + C II. B. ['dr + C…

A: As we know that; The Power rule; ∫ax+bndx=ax+bn+1an+1+C ; n≠-1 And ∫eax+bdx=1aeax+b+C…

Q: Find the area bounded by these curves. (All choices are in sq. units) y = x? y = 4x – x2

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Q: X1 – 4x, + X3 = 2 4x1 + X2 =1 Xz + 4x3 =-1

A: Since the question is asked to solve by two different method solution by one of the method is given…

Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y+3…

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Q: 3. y = Arccos ( logx);y' = * O -1/x In(10)*sqrt ( 1 - (logx)^2) O 1/ x In(10)*sqrt (1 - (logx)^2) O…

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Q: (29.4) Determine whether the series (-1)"-1. n2 + 1 is absolutely convergent, condi- n=1 tionally…

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Q: A) If (xn) is a decreasing and bounded sequence. Prove that (xn) is convergent with lim xn = inf {xn…

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Q: Find two unit vectors in 2-space that make an angle of 45° with 9i + 4j. NOTE: Enter the exact…

A: Solution: Let u = ai+bj makes an angle of 45 degree with v = 9i +4j

Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

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Q: Find the volume of the solid formed by revolving the region bounded by the curves x=2√y, y=0, and…

A: The graph is shown below, where the chex region represent the required volume to find.

Q: 4. CHOOSE one of the following functions (CIRCLE YOUR CHOICE): y = 2 log(x + 3) – 5 Asymptote(s)…

A: As per our guidelines, we can answer only three sub-parts in a single request. Kindly re-post the…

Q: Consider the mass-spring system for mass 0.5 kg, spring constant 4.8 N/m, and an oscillating force…

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Q: Verify that the two planes are parallel. -x + 6y + 3z = 7 x+ 2y + z = 8 Find the normal vector, n,,…

A: Normal vector of a plane Ax+By+Cz+D=0 is defined as A, B, C

Q: Find an equation of the plane through (0, –9, –1) that is perpendicular to the line x – 2 = 3t, y +…

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Q: Consider the points A(3, –3, 2), B(4,–5,0), C(-1, –4,0), and D(6, 2, –3). (a) Find the volume of the…

A: AB→ = i -2j-2kAC→ = -4i-j-2kAD→ = 3i+5j-5k Volume of parallelepiped with AB→, AC→ ,AD→ as adjacent…

Q: S 4x cos(2 – 3x) dx

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Q: Perpendicular to each of the planes x – z+ y = 0 and 2x + z – 4y = 5 and containing the point (4,…

A: We have to find an equation of the plane which is perpendicular to each of the planes x-z+y=0 and…

Q: The function f(x) = x + eª has one real zero x0. In which of the following intervals must xo lie? А.…

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