What is the equation of the line Lz pass through the point ( 2,-1) that is parallel to the line L, which has equation 2X + 4Y 12

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A: This is a problem of differentiation. Please follow the procedure given below. 

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Q: Integrate S(cos x)e*+sin xdx B. et-sinx + C A. -e4+sin x + C c. e4+sinx + C D. e-4+sinx +C A В C D

A: Given: I=∫cosxe4+sinxdx  ....(1)   We know that; ∫eax+bdx=1aeax+b+C

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Q: dy 1. Use logarithmic differentiation to find given that dx sec-1(Vx) 4sech(5x)(log6 x)* y =

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Q: Given f(x,y) = 4x sin(5xy). Find fy(4,5). Give you answer correct to two decimal places. Answer:

A: The objective is to find the above partial derivative at the point (4, 5).

Q: Given f(x) = -2x + 4 and x = 3r ln (4s). Find fr (5, 3). Give your answer correct to two decimal pla...

A: Given; f(x) = -2x + 4 and x = 3r ln (4s).

Q: If the integral contains v(x^2 - a^2), the best trigonometric substitution to be used is A. let x = ...

A: Solution is written in below steps.

Q: cos? r dr ? 1+2? The improper integral since, cos z A. 1+z2 1 for z>1 and / 1 dz 1 +1 r2 + 4 cos z c...

A: The objective is to find the correct option.

Q: 1. In the figure shown, a vertical triangular gate submerged in a certain liquid with s.g. = 0,85. I...

A: We have to find 'd'. 

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Q: Evaluate the integral. (Use C for the constant of integration.) | sz?e" dz

A: ∫5z3ezdzusing integration by part ∫fxgxdx=fx∫gxdx-∫dfx∫gxdxdxNow, fx=5z3,gx=ez∫5z3ezdz=5z3∫ezdz-∫d5z...

Q: Question: * Using integration by parts, integrate S In 5x dx A. xln 5x – x+ c с. 5xInx - х+ с в. х? ...

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Q: x? dx and simplify your answer. Show your

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Q: Find the area of the region that lies inside both the curves r = sin(0) and r= cos(0). A. (M В. (п 2...

A: This is a problem of integration. We will calculate the area by using integral method. Please follow...

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Q: Find the maximum and minimum values of the function f(x) = In(x) on the interval [1,6] by comparing ...

A: Solution ) f(x) = lnx/x f'(x)=  [x (d/dx ( lnx )) - lnx (d/dx (x) )]/ x2 By differentiation divisibi...

Q: the Standard iom TocI. he standal the equation (Type an equation. Simplify your answer.) (-1,1) -4

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Q: 2. Solve the following differential equations. (a) y' = x2 – xy+ 1. (Hint: Consider the subsitution ...

A: Both the parts have been solved in detail. 

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Q: Consider the region bounded by x = 1+ 4y – y? and x = 4. a. Compute for the end points of the region...

A: (a) computing the end pointintersection point between x=1+4y-y2 and x=44=1+4y-y2y2-4y+3=0y2-3y-y+3=0...

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Q: Find the length of the curve y = In (1 – 2*) over the interval [-,].

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Q: Evaluate the integral: tejat A. 2 1n(e2t-e-2t) +C B. 2 1n(e2t + e¬2t) +C e20-e-2t In(e2t-e-2t) +c - ...

A: To evaluate the given integral.

Q: Let an​ be an arithmetic progression, for which a2​=5 and a1​=−11. Find the difference of the progre...

A: The objective is to find  the difference of the progression.

Q: EXPLAIN ON HOW YOU WILL SOLVE FOR THE LIMITS OF TRANSCENDENTAL FUNCTIONS USING TABLE OF VALUES AND G...

A: This is a problem of limit of function. By using the left hand side and right hand side limit we wil...

Q: 3. Apply the partial fraction decomposition to evaluate the integral 4-x2 x(x2 + 2) x

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Q: Use Bisection Method to find the root of æ + 10x? – 5 0 that lies in the interval (0, 1) to four-dig...

A: We have to find the root of the given cubic equation using bisection method.

Q: Q2: Sketch the polar function r = 6 cos 30 ,-n < 0 < n|

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Q: Find the gradient of the function at the given point. f(x, y) = 5x + 3y2 + 5, (4, 1) Vf(4, 1) =

A: f(x,y)=5x+3y2+5 fx(x,y,z)=5fy(x,y,z)=3(2y)=6y∇f =fx(x,y,z) i +fy(x,y,z) j

Q: For the given cost function C(x)=40000+700x+x2C(x)=40000+700x+x2, First, find the average cost func...

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Q: Evaluate f sec x dx.

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Q: Find the volume of the solid of revolution obtained by revolving the region bounded by y = x - x^2 a...

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Q: + y*)dx dy B. 19/2 Evaluate A. 35/2 C. 37/2 D. 17/2 A

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Q: Suppose the Sunglasses Hut Company has a profit function given by P(q)=−0.03q2+4q−46P(q)=-0.03q2+4q-...

A: This question can be solved using the concept of maxima and minima.

Q: A certain TV program earns a rating of 11.5, in a time period when 57.3% of television households ar...

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Q: 1. Find the derivative of f(x) = x² – 3x. Use the result to find the slope of the tangent line to th...

A: Since you have posted multiple questions in this question which are not interlinked so I have solved...