Q3 (A): By using "L' Hopital rales "; Find the limits of: (1) limal; (2) Itm X(tan-¹x-x)

Q: sin 8 cose √cos²0-9 S do

A: Our Aim is to evaluate the integral given below:-∫sin θcos θcos2 θ-9dθ -(i)

Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: Given the ODE (cscy)dx + (cos²x)dy = 0. A one-parameter solution of it is: O cosy + tanx = c siny =…

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Q: dy 5: Find for the following functions: dx (1) In (x - y) = xy + y³; (2) y = tan³ √/cot(7x); (4) y =…

A: Since we are given with multiple number of question and answered according to the guideline

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A: Given: Initial amount =$5000 Increase amount =$900 Time =2 years To find: Rate of increase at the…

Q: Find the volume of the solid that lies under the plane 3x + 2y + z = 12 and above the rectangle. R=…

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Q: 9x¹+x x-100 2x¹45x²-x+6 iv. lim

A: Given limx→∞ 9x4+x2x4+5x2-x+6

Q: (B): Find the tangent equation to the curve y = sin² x at point x =

A: I have stated the used formulas in the solution.

Q: Determine the intervals on which f'(x) is positive and negative, assuming that given figure is the…

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Q: 1. y = Arccos 1-x

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Q: Q2: Solve the following integral (1) 7x²+14x+15 (x²+3)(x+7) dx dx ; (2)

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Q: Given f(x) = 3x² Rn = 6, find a formula for Rn on the interval [2, 5]

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Q: dw (C): If w = tanx and x = 4t³ + t ; Find dt dy

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Q: 3. 2 洲 dx

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Q: Q3 :(A): By using " L' Hopital rules "; Find the limits of: 1 2 (1) limx-o[: 1-cos x sin²x (2)…

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Q: Evaluate the function at the given values of the independent variables. Simplify the results. f(x,…

A: Topic = Functions

Q: Which of the following statements is/are true based on the graph of the function f(x) = -2(-x-²) +…

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Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

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Q: Find the volume of a solid of revolution formed by revolving the region bounded by the graphs of…

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Q: Find all the zeros. Write the answer in exact form. 4 q (x) = 2x² +9x³-5x²-57x-45 If there is more…

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Q: dy Q5: Find for the following functions: dx (3) y = ex.sin² x In√x

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Q: Write a polynomial f(x) that meets the given conditions. Answers may vary. Degree 3 polynomial with…

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Q: 15,0-20³²4 2. 3. चं 5. T cos 2x dx sin(³) cos²( :-) / dx 2x - 1 4x dx dx 6. 7. [² (x² + 0²³) dx (x -…

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Q: find the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2

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Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: We have to find out equation of tangent

Q: The pH can be calculated using the equation pH = -log(H"), where H" is the hydronium ion…

A: We can find the hydronium ion concentration as below.

Q: First, compute the gradient of the function f(x,y) = 4+5x²-3y². Then evaluate it at the point…

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Q: Apply Descartes' Rule of Signs. Determine the number of possible positive and negative real zeros…

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Q: (B): Find the unit vector 3i - 4j + 5k perpendicular to the vectors: 4i + 5j-6k

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Q: 12. (2xy³ + 1) dx + (3x²y²-y¹) dy = 0

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Q: Q2: Solve the following dx 7x³+14x+15 (x+3)(x+7) 1735 (1) J inte (2

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What is the area of the region between  y=x^2 -2x-3 and the x-axis from x=0 to 6?

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Q: cos¹3 xdx 2. Dễ sin12xcos®xdx 1.

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Q: Use the given acceleration function to find the velocity vector v(t), and position vector r(t). Then…

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Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(0) and y = r sin(0), and note that (x,…

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Q: k [[ x=0&y=0 x cos(xy) dydx =

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Q: Find the first partial derivatives of the following function. f(x,y)=x²-3xy-6y²

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Q: Find the point (if it exists) at which the following plane and curve intersect. z = 19; r(t) = (t,…

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Q: nd the limit, if it exists. If the limit does not exist, explain why. limx→2 1−|x|^2/1−x^2 You…

A: Given :limx→21-x21-x2

Q: dx d dx dx d dx -sinu d dx -tanu dx dx d dx d dx COSU dx cot u secu CSCU √u A.n+un- B. au* Ina*. C.…

A: Please see the below picture for detailed solution.

Q: y = sin(x), y = 0, x=0, x= π Exercise (a) the volume of the solid formed by revolving the region…

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Q: Evaluate the following integral. 45 S SS²² dz dx dy -411

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Q: 3. 31 √ √(²x- (2x - 4y)dydx 1 -1

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: A solid of revolution is formed by revolving about the x - axis the region bounded by the curve y =…

A: Topic = Volume

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Q: Find a result by using exact for (sinxcosy)dx = -(cosxsiny)dy = 0 b. (x-6xy + y² + 10)dy = -(x² -…

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

Q: 4. A one-way road has an overpass in the form of a semi-ellipse, 15 feet high at the center, 40 feet…

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Q: 900mL of lactated ringers is infusing at a rate of 42gtt/min.  The drop factor is 60gtt/mL.  How…

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Q: Apply Descartes' Rule of Signs. Determine the number of possible positive and negative real zeros…

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