10. At what point on the parabola y = 3 x 2 + 2xisthetangentlineparallel totheline y = 10x -2? Use first principles in your solution.

Q: Plot the curve r = 1+sin 8. Then find the length of the curve.

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Q: 2 30 مر ول 2 + 6 +

A: In this question we have to solve the Integration.

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Q: Solve the following a) 2d²y_dy 3y = 25 sin 2x dx² dx d²y b) - 4 - 3y = 25 sin 2x dx² dx c) d²y dx² +…

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Q: Use the indicated methods to approximate the area under the curve f(x)=x²-1 on the interval [2, 5].…

A: Here we have to find the area.

Q: 4. Find the absolute extrema for the function f(x)= on the interval -5 ≤x≤0.

A: To find the absolute extrema of the given function in the interval [-5,0].

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Q: Use Descartes' Rule of Signs to determine how many positive and how many negative real zeros the…

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Q: ch, choose its equation from the following. = sec (x+²) = y = cot (x + ²) 4 v=2 tan x 2 y=-csc x 1 T…

A: we have to find the graph

Q: Find the slope of the tangent line to the curve 4x² 3xy - 2y³ = - 26 - at the point (4, 3).

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Q: Graph the function using translations. f(x) = 3x+1

A: We will find the suitable graph.

Q: 5. Does the function f(x) = If yes, what are they? If no, explain your reasoning. have absolute…

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Q: The estimated monthly sales of Mona Lisa paint-by-number sets is given by the formula q = 98e-3p² +…

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Q: A circle has a radius of 3.5in. A sector of the circle has a central angle of 1.5 radians. Find the…

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Q: eſt 2 du given that * f(z) dx = 12 f(4Tan¹(u)) 1+u² Evaluate

A: Hint :  This problem is application method of substitution in definite integral. If you have not…

Q: Write an equation in vertex form of the parabola that has the same shape as the graph of f(x) = 9x²,…

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Q: 6. Find the intervals on [0,27) where f(0) = sin² (0) is concave upward/ concave downward.

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Q: x2 (x− 1)(x4 +8x²+16) dx- S

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Q: Consider the following. (1, 1) 2 6 10 X 4 X=8 -4 y = 2-x -6 -8F (a) Form the integral that…

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Q: 7) Two ships are leaving port at the same time. The first ship sails due east at 20 km/h, the second…

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Q: * (2 √x (2+x) dx

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Q: f(x) = e²x cos(x) e2

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Q: Use the formula к(t) 390 t¹4 k(t) (4 + 210 t¹3) = ||r'(t) × r"(t)|| ||r' (t)||³ = r(t) = t²i+t¹5j X…

A: Use derivative for finding the curvature .

Q: dx x²+2x+5

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Q: ) Suppose F'(x) = 2x² + ex and F (4) = 1. Find the value for F(b) for b = 8.

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Q: S ex √1-e²x dx

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your answer to two decimal places when…

A: We have to find the value

Q: Evaluate (sin² (sin² x cos x)(1+ sin z cos x) dx.

A: Use substitution method

Q: Consider the following matrix. -2 -3 A = 5 7 Choose the correct description of A. Find A if it…

A: First check that given matrix is singular or not then find its inverse.

Q: "alse 1. The absolute extrema for a function f(x) will occur wherever f'(x) = 0 2. The rectangle…

A: Topic:- function

Q: Use Cramer's Rule to solve this system of linear equations: x+y+z=3 4x-y+z=0 -7x-y + 2z = -3 Find…

A: The equations can be written as;1114-11-7-12 xyz=30-3D=1114-11-7-12   =1(-2+1)-1(8+7)+1(-4-7)…

Q: Sketch the region whose area is given by the integral and evaluate it. Answer: 8 sin 0 Lote Lor r dr…

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Q: 1. If z = f(x, y) has continuous second-order partial derivatives and x = r cos 0, y = r sin 0,…

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Q: x²+4x+10 x3+2x²+5x dx

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Q: 1.57 1 (1.5,2) (-0.7,02) (0.7,0.2) -1.5 -0.5 1 1.5 --0.5+ -1.5 Where does f have absolute minimums?…

A: Recall:  In graph, y-coordinate at the lowest and highest points are called the absolute minimum and…

Q: 4 P = 80x-2x²-xy-3y² +100y + X(12-X-Y) FinD Px, Pxx, Py, Pyy, Pxy = Pyx, fino x And y Fine Fine P

A: Here's the solution.... please have a look at it...

Q: 1. Use the limit definition of derivative (no shortcuts!) to find the derivative of f(x) = 3x² + 2x.

A: The formula for derivative of function f(x) using limit is given by:…

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Q: S sin (3x) 1+cos² (3x) dx

A: The detailed solution is given below Thank you

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Q: 17 m K 19 m hm 9 m Part 1: Part 2: Part 3: Part 4: Let h be the height of AJKL. Find the length of…

A: To find the area of triangle, height etc..