1. Simplify the expression, that is, rewrite the following expressions as algebraic expressions of x. (a) sec (arctan (;)) (b) cos s (2 sin−¹ (√x² − 1))

Q: Evaluate the iterated integral **²y³ dady.

A: K=∫04∫016x2y3dxdywe know ∫xndx=xn+1n+1+c

Q: A function y = g(x) has a derivative shown below for -3 ≤ x ≤ 3. Three -3 O Four 312 3 (b) Where is…

A: Answer: The solution is given below:

Q: Find the derivate of this function]: a) f(x)= 9x²³+24x² - T F'(x) = b) f(x) = 4x³ + 9x²-9. F'(x) =…

A: (a)  f(x)=9x3+24x2-πd dx(xn)=nxn-1d dx(constant)=0

Q: The number of cell structures in a Minbari stem cell (fictional) is modeled by f(t) = 1 + 30t - 10t³…

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Q: Find the derivative of the function. F(t) = e5tsin(2t) F'(t) =

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Q: A region R is shown. Decide whether to use polar coordinates or rectangular coordinates and write…

A: given shaded region is between concentric circles with radius r=8 and r=10. So, it is better to use…

Q: Show that the lines L₁ : x = 1 -t, y = 2t, z = 5 + t and L₂: x=1+3t, y = 3-6t, z = 5-3t are parallel…

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Q: Find the critical points in the domain of the function f(x) = 8x³ - 7x.

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Q: Use Lagrange Multipliers to find the maximum value of f(x, y, z) = 2x + 2y + z, subject to the…

A: NOTE: Refresh your page if you can't see any equations. . the given function is find the partial…

Q: Find the distance between the point and the plane. (Round your answer to three decimal places.) (4,…

A: To Find : Distance of point (4,6,3) from the plane x-y+2z=10

Q: cos* xdx

A: To evaluate the following integral. ∫cos4x dx

Q: 3. Determine whether the series is convergent or divergent. State which test for convergence or…

A: SOLUTION: Given that ∑k=1∞ke-k2 Now we have to determine whether the series is convergent or not .…

Q: Find the first and second derivatives of the function. Check to see that your answers are reasonable…

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Q: Which of the following could be the slope field for the differential equation B MAZZ ~~X1/17 71XSS…

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Q: Use linear approximation to estimate the value of the following  cos(pi/4 +0.01)

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Q: 3 2 x+カーカー1 カナ 七 -1)dx

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Q: Find the particular solution to the given differential equation that satisfies the given conditions.…

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Q: Skecth the graph find the area of the region a. r=a, a>0 b. r = 2+cos 8

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Q: Let f be the function with domain [1, 3], defined by f(x) = −x² + 3x. The function f has a global…

A: The answer is in step 2.

Q: Let r(t) = (5t51, - 4e5t, 2 sin(t)) Find the unit tangent vector F(t) at the point t = 0 T(0) =

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Q: Determine the volume of the region bounded by y=x^(2)-2x and y=x that is rotated about y=4

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Q: Use a triple integral to find the volume of the given solid. The tetrahedron enclosed by the…

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Q: What is the x-value and y-value of the point of intersection of y=-3x+10 and y=2x-5?

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Q: Evaluate the given integral by changing to polar coordinates. 160-x²-1² dA, where D is the region…

A: Consider the provided question, We need to evaluate the integral  ∬De-x2-y2dA by changing to polar…

Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. y = x3, 0 ≤ x…

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Q: Using substitution differential equations. methods to solve homogeneous Y'= Y+X

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Q: (d) 4x²y" + y = 0, (e) y" + 16y = 0, Y₁ = √√x ln x Yı Y₁ = cos(4x)

A: see below the answer and calculation

Q: •Evaluate the ff. dx 3x²+12x+15 T.

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Q: 7. Integrate the function 4ry³ over the region bounded by y = x, x=2, y = 0. (2.2) (0,0) (2,0)

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Q: 7. Find dy fo dx for x³ -y + y² = 4.

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Q: Differentiate f and find the domain of f. (Enter the domain in interval notation.) f(x) = = domain X…

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Q: Express the given parametric equations of a line using bracket notation and also using i, j, k…

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Q: Let a = (4, 0, 5) and 6 = ( − 3, − 1, 1). - Find the projection of b onto a. projā b = < Calculator…

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Q: Find the derivative of the function at the given number. f(x) = √x at 25 f'(25) =

A: To find the derivative of the function at the given number. fx=x at 25

Q: Find the position vector for a particle with acceleration, initial velocity, and initial position…

A: I have done solution step by step in detail ....go through the solution

Q: 2. Determine whether the series is convergent or divergent. If it is convergent, find its sum. ܐ 5…

A: The Series ∑n=0∞arn is called geometric series and the geometric series a is the first term and r is…

Q: Can you draw a line tangent to the graph of f at the specified point and estimate the slope of this…

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Q: A flagpole is 40 feet high and stands on level ground. A flag is attached to a 120 foot rope passing…

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Q: Determine whether the planes are parallel, orthogonal, or neither. 3x 15y 3z = 8 4x20y4z = -2 - O…

A: Two lines are parallel if the ratio between their corresponding coefficients is same. The angle…

Q: Find the following limit. lim V

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Q: Where does the line x = 4+t, y = 7-t, z = 2t intersect the cylinder x² + y² = 121? Enter your…

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Q: Find the center of mass of a thin triangular plate bounded by the y-axis and the lines y=x and y=2-x…

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Q: (d) B dy dx 1- x - y x + y

A: ode

Q: The differentiable functions f and g are defined for all real numbers x. Values of f, f, g, and g'…

A: Derivative

Q: picture of your 2-Dimensional region to support your limits of integration SET UP the double…

A: To find the double integral to calculate the area.

Q: Find the elasticity of demand (E) for the given demand function at the indicated values of p. Is the…

A: The given demand function is: g=408-0.3p

Q: You are given the circle, x² + y2 = 25.

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Q: Consider Line 1 with the equation: y= (1)/(2)x+9 Give the equation of the line parallel to Line 1…

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Q: Find the area of the parallelogram with vertices A(-5, 5), B(−3, 8), C(1, 6), and D(-1, 3).

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Q: Find the distance from the point (7,1,-2) to the line ä(t) = (-5, 0, -2)t + (0, 3, 6). Calculator…

A: We have to find the distance between the point and line.