(a) Find the general solution of the differential equation d²y dx² +9y = x² + x + 1.

Q: 1. IF PLx) =5х4 Sox2+9х2 Find F'(x) and F'(2)

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Q: Find the derivative of the function using implicit differentiation. 1.) x²+y²= 16

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: This question is designed to be answered without a calculator. A farm has a rectangular pigpen that…

A: Let's find total numbers of pigs in the piggen.

Q: 9.) Find all horizontal and vertical asymptotes of f(x) = 4x 5 - x² - 9

A: The given function is f(x)=4x-5x2-9 First we factorize the numerator and the denominator.…

Q: • Evaluate the following integrals: Convert this Cartesian equation (x² + y²)²_9(x² - y²) = 0 to…

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Q: -5e-cos2t O Option 4 5e-t sin 2t O Option 2 5e¹ cos2t O Option 3 5e sin 2t O Option 1

A: Topic:- application of derivatives and integration

Q: {CLO-3} The critical number(s), if any, of the function O -1. 12.2 01/14 2 O 0, 1, 2 O There is no…

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Q: The doubling time of an investment with continuous compound interest is 12.5 years. If the…

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Q: 4. Calculate the average value of each function over the given interval. Hint: use the identity sec²…

A: Average is evaluated.

Q: 2. Consider the function f(r). 2r²-9r-18 r²-r-2 (a) Sketch the curve y = f(r). (b) Find the area of…

A: We have to sketch the curve and find area.

Q: 1.) Find the area of the region bounded by the curve ya 12 and the lines y=o, y=x, x=2.

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Q: .

A: Please refer to the image below

Q: This question is designed to be answered without a calculator. Use this graph of function f. y 5+ in…

A: Here, from the given graph the function is continuous at x=0,2,4 but not continuous at x=-2 because…

Q: 2 (0) IF F(x)= x 'e', Find f'(x) and F (1)

A: Finding the derivative of the function.

Q: Find the volume of the solid generated by the revolving Shaded about region the 7-axis 1 0.5 X =…

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Q: Additional Activities (-2.39) a 4 88/88 20 10 10 -20 30 40 1 (2.7 Solve the following problems. A.…

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Q: s-1 s(s+ 1)² -1+et+2te-t 2+te-t-e-t O Option 1 Option 3 1+et-2te-t Option 2 -2+tet + et O Option 4

A:

Q: η3+n2 (5) Σ=o (n+1)!

A: Series ∑n=0∞ n3+n2n+1!

Q: Find the equation of the line tangent to 2exy = x + y at the point (2, 0) Write the equation in…

A: Given query is to find the equation of the tangent at given point.

Q: (CLO-3) Find the absolute maximum value of the function f(x)=x³-12x+3 on the closed interval [-4,3].

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Q: Find the radius of convergence for the series 3 n³ xn 3n OR=3 O O OR= 8 n=1 R = R= - الله R = 1 8

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Q: [CLO-3] The second derivative f"(x) of a function is given. Use this information to find all values…

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Q: Find the derivative of the function at Po in the direction of u. g(x,y)= x-y 3xy + 2' Po(-1,1), u…

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Q: (4) Σ=o (−1)n+7 n2+3 1/1

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Q: This question is designed to be answered without a calculator. (10¹ x) = (In x)10¹n x-1 O (In…

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Q: 17. What is the amplitude of the graph y = -4sin (x - 2)? The amplitude is. units. 04 02 O 2T O K|N…

A: For the equation  y=A sinBx+C+D   A-  Amplitude   B- Frequency   C- Horizontal shift   D-  Vertical…

Q: dy 5. Use Implicit Differentiation to find dx a) 4xy + x² = 4 - Iny³

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Q: Find Vf at the given point. f(x,y,z) = x² + y² − 4z² + z lnx, (1,1,3) Vf|(1,1,3) = i +(\)j + ()k…

A: Given the function,   fx,y,z=x2+y2-4z2+z lnx

Q: If the equation F(x,y,z) = 0 determines z as a differentiable function of x and y, then, at the…

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Q: To find the distance across a small lake, a surveyor has taken the measurements shown. Find the…

A: As per guideline we can answer only one question, Please repost other question.

Q: Given the following functions: Find: f(j(x)) f(x) = 3x² - 5x+2 g(x) = 7x² + 3x - 1 2x - 7 h(x) 5x -…

A: Given query is to find the Indicated composite function.

Q: Evaluate lim zo the limit sin 7x sin 2x

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Q: Consider the functions z= - ex In y, x= In (u cos v), and y = u sin v. dz dz (a) Express and as…

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Q: The critical number(s), if any, of the function f(x) = (x²-3x+2) is (are):

A: critical points of fx=x2-3x+2-13

Q: Numbers 10,11,12 please

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Q: Sketch the graph of the piecewise defined function: f(x) = 2, x ≤ −1          x − 1, x > −1

A: Given  f(x) = {2,   x≤-1              x-1, x>-1}

Q: Use the shell Method to Find the Volume of the bounded by Solid generated by by revolving the region…

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Q: Use linear approximation, i.e. the tangent line, to approximate √25.2 as follows: Let f(x)=√x. Find…

A: Linear approximation for fx=x at a=25The linear approximation of the function fx at point a is Lx =…

Q: 9. f(x) = xe−2*, a = 0

A: According to bartleby guidelines I can only answer the first question of the two given.

Q: Find the equation of the tangent line to the function f(x) = 5* at x = 4. (Use symbolic notation and…

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Q: Find the domain of =) = √x² – 3x

A: Given query is to find the domain of the function.

Q: Find the derivative of the function at Po in the direction of A. f(x,y)=-3xy + 5y², P₁(-10,2),…

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Q: If à = 3ai +4j-k and B = 4i+j−3k, find the value of a if A normal to B.

A: Given vectors A→=3ai+4j-k and B→=4i+j-3k

Q: [CLO-3] The second derivative f"(x) of a function is given. Use this information to determine where…

A:

Q: Suppose that sin(θ)=4/6. What cos(θ)=______. (round to 3 decimal places)

A: sin(θ)=4/6

Q: Syy-mat sama dy ³

A: Follow the procedure given below.

Q: 3. Suppose a function H(t) is given and that this function describes the height H of a projectile t…

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Q: Determine the limit of the sequence or state that the sequence diverges. 6 an = 1- n² (Use symbolic…

A: topic- limits

Q: Find the volume of the solid generated when the plane region bounded by: x=y^2 and x+y=2 is…

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

Q: 6) (-2√2,2√2) 3 3√3 8) 2 10) (-2,-2√3)

A: