Find the derivative of the following:

Q: 4. Find the area between y=Z+3. and ys-xt1ox-9

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Q: If S; (x²-1)(2x-x*) dx can be resolved into A S+ B S f(x)dx + D S g(x)dx , then x²+x-2 lim, ° dx +…

A: Partial fractions: The fractions needed to decompose a rational equation are called partial…

Q: Find the length of the curve. 9) The spiral r = 202, 0 s 0 s 2^/3

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Q: If z = +3y, find the differential dz. dz =

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Q: Using the function f(x, y) find the following limits. If a limit does not exist, enter DNE. z* + 5y2…

A: On solving this we will get

Q: 5. IF sin@=5 =E and@inthe first quadrant, find cos

A: We have to find the cos angle

Q: If x= tane , then dr = coso de . (1+x?)½ A True B) False

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Q: Use Lagrange multipliers to find the point on the plane x – 2y+ 3z = 6 that is closest to the point…

A: Let, the point be (x,y,z) then the distance between (x,y,z) & (0,1,4) is:…

Q: Find the sum of the geometric series. 2.5 15 25

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Q: V4.01 V4.01 Give your answer correct to Use differential to estimate the value four decimal places.…

A: topic- differentials

Q: Problem 7. Solve the equation logx+log(x+1) = log12 and leave your answer in exact value

A: Solve for the value of X

Q: 7. An analyst has found that Tom's Transmissions Company cost function is: C(x) = 40,000 + 500x –…

A: As per Bartleby answering guidelines if a questions has multiple subparts then an expert is expected…

Q: ea da (ea + 1)Ve2a + 2eª

A: Given

Q: 24. (EXERCISE) Consider the function f(x)=3x* – 20x' + 42x² – 36x

A: The given function,   f(x)=3x4-20x3+42x2-36x

Q: dy a) If all of y = 4n2 + 5n + 1,x 3n + 2 find dx b) if yx2+Vx + xy? = 1 prove that = -at (1,-1)

A: Please see the answer below.

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the…

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Q: 3n 8 If tan 0= find the exact value of each of the following. 2 cos (20)

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Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: ry+2 4- (4x2 - ay) dx dy

A:

Q: Find the direction angle of v for the following Vel v = - 6i- 3j What is the direction angle of v?

A: On solving this we will get

Q: Given sin 0=- determine all possible values of 0 over the interval [-2n, 2n]. 2'

A: Given query is to find the value of the Indicated angle.

Q: 1. Find a power series representation of In(1+x²) and determine the radius of convergence. Eind the…

A: 1.

Q: Determina the vector field of F. F(1, y) = yi -j

A: Please see the below picture for solution.

Q: Calculate the following derivative if f(x) = 5e* - x³. %3D (Use symbolic notation and fractions…

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Q: y = xx, x=4, and y =0 Revolve the area of the shaded region about the line x = 4. Using circular…

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

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Q: If f(x) = 8+r dt, find f(1).

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Q: Determine the area of the gtven reglon. y = x + sin X Step 1 Note that for the glven reglon, x…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find (a) the critical numbers of f (if any) (b) the open intervals on which the function is…

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Q: Find the equation of the tangent line to y=(3x+4)3 at the point where x= -2

A: here given y= (3x+4)3 slope  of the tangent line is y'    Here y' = 9(3x+4)²   Value of y at x=-2 is…

Q: Find the limit. If the limit does not exist, type DNE. lim (1,9) →(-4, -2) 32 – 5zy =

A:

Q: Find the differential dy and evaluate dy for the given values of x and d.x y = Vx2 + 24, x = 1, dx =…

A: First differentiate with respect to x then find value at x=1 and dx=-0.1

Q: Question 21 (-1 )dr In (z + a+ 1) + v3 sin In ( + + 1)-3 tan O 2 In(z +a + 1)-V3 sin () 2 lu(r i…

A:

Q: | 5f(x)dr c f(r)dx if c =

A: Given :∫725f(x)dx=c∫27f(x)dx

Q: -9 2. They" for y V3x-5

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. (8t – 1)2 dt 0.

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Q: A line is given by the equation y = x in rectangular coordinates. V3 Which of the following…

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Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

A: solution:-limx→1sinx-1x3+4x-5 ,  it is  00   formusing  L'Hospital's…

Q: (cos(x)) dx cos(c) 3.

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Q: Find div F and curl F if F(x, y, z) = 14y°z4i – 3x°z+j – 3xy'k. %3D div F= curl F=

A: Given that,Fx,y,z=14y6z4i-3x3z4j-3xy3k

Q: Find the area of the triangle. Round to the nearest tenth. A 61° 13 mi 7.2 mi C В 14.3 mi? 12.6 mi?…

A: Given query is to find the area of the triangle.

Q: Type the correct answer in each box. Create a matrix for this linear system: (3x+2y+z D26 I-4y -11…

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Q: 3 In ДАВС, с % 15 ст, b — 4.6 ст, тLA: = 106°. Find the area of the triangle and round to the…

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Q: 12 (25x – 46x' + 3)dx J-12

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Q: EXAMPLE 1: Consider the graph of the function f given below. Using the given graph, determine if the…

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Q: 15x + 44 -5x + 84=26 then astructions: Rewrite each Systems of equatons as amatrix, perform cow…

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Q: integral

A: We will solve the definite integral.

Q: V100-1000 lim y-10

A:

Q: 6. If z = a+i is a root of the equation z² – 6z + 10 = 0, find the value of a, if a is a real %3D…

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Q: lim sec x x-(-71/2)"

A: