Verify the integration formula. S 6 sechx dx = tan-1 (sinh 6x) + C (A) No B) Yes

Q: 8 4 4 -7 (a) h(x) = 7X 1 -7 (b) g(x) = 7x (c) k(x) = - 7X %3D %3!

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Q: %3D Find the maximum value of the function f(x) =x° - 9x2 + 15x - 5. Answer: Find the value of x for…

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Q: der the following planes. 5x + 2y – z = 44 x – 4y + 2z = 0 (a) Find the angle between the two…

A: Angle between planes and line of intersection of planes

Q: 2. State the domain, range, asymptotes and graph the following function 4x-3 x+4 lity: Investigate…

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

Q: Each side of a square is increasing at the rate of 8 cm/sec. At what rate is the area of the square…

A: Solution :let, side of square=xArea of square=Adxdt= 8 cm/secA= 36 sq. cmA=x2    Area of square=side…

Q: Sy-2+1 dy 2.

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Q: Vx- 2 Evaluate lim x-8 x2-7x-8 O 2/7 None of these O 1/9 O 1/12 O O o O

A: The given limit,     limx→8x3-2x2-7x-8

Q: If f(x) = e%g(x), where g(0) = 5 and g'(0) = 2, find f '(0). %3D

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Q: xdx Evaluate (x²-2)5

A: Given query is to evaluate the integral.

Q: Let the region R be the area enclosed the function f(x) = x², the horizontal line 6, and the y-axis.…

A: Explained below

Q: Suppose the position of a particle is given by parametric equations x(t) = 2t2-1 and y(t) = 3t3. (a)…

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Q: Find the most general antiderivative or indefinite integral. csc 30 de csc 30 - sin 30

A: The objective is to evaluate the integral.

Q: (8x3 + 2x) dx = 2x4 + x² Select one: O True O False (sinx/cos-x)dx = sec x + C Select one: O True O…

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Q: Given the graph of the function below. Find the limit of the functic approaches 3.* (3, 4) (0,3)…

A: Given query is to find indicated limit.

Q: Find an equation of the tangent plane to the surface at the given point. f(x, y) = x² – 2xy + y²,…

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Q: he power supply of a satellite is a radioisotope (radioactive substance). The power output P, in…

A: Given: The power supply of a satellite is a radioisotope radioactive substance. The power output P,…

Q: Find the iimit oT X SP approaches zero from the left. x -3.62330136 t-0.827974189 4- 2 10 12 does…

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Q: (3 - 2 3 – 4cos dx

A: The given integration,     ∫3-4cosxπ2 dx

Q: Example 2 Compute (a) (1+i)/(3-i) and (b) (1+i)4.

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Q: Convert - 240° to its radian measure.

A: Given  240°

Q: Solve the differential equation. (x² + 15)y' = xy

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Q: A bacteria culture is known to grow at a rate proportional to the amount present. After 60 minutes,…

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Q: Use the cylindrical shell method to calculate the exact volume of the solid formed by rotating the…

A: Solved below

Q: A stellar object is emitting radiation at 1820 nm. A detector is capturing 7 x 10' photons per…

A: Please refer to the image below

Q: Differentiate. f(x) = - 2 e -X t'(x) = ]

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Q: dx x'+3 Xん X

A: We have to solve the integral.

Q: The shaded region shown below is bounded by the functions f(x) = -3x2 + 8 and g(x) = 0.5x + 6 and…

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Q: A student throws a ball upward from a height of 48 feet, initially at 32 ft/sec. The function that…

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Q: Integrating Factor by Formulas: (4) (4xy + 3y² – x)dx + x(x + 2y)dy = 0 (5) y(x + y + 1)dx + x(x +…

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Q: The sum of two numbers is 8. The product of the first number and the square of the second number is…

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Q: Differentiate. 12 f(x) = 17 f'(x) =|

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Q: Find the gradient of the function at the given point. Function Point f(x, y, z) = Vx2 + y2 + z? (4,…

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Q: Find the dimensions of a rectangle with area 216 m whose perimeter is as small as possible. (If both…

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Q: (Rounded to the nearest hundredth) Use the cylindrical shell method to calculate the volume of the…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. xyz = 20, (1, 4, 5) (b)…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Use the cylindrical shell method to calculate the volume of the solid formed by rotating the graph…

A: To solve the following problem

Q: The sum of two positive numbers is 20. Find the product of the two numbers if the sum of their…

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Q: The equation of the line tangent to the differentiable and invertible function f(x) at the point (5,…

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Q: with A parti cle is moving a cc eleratoN at) = 12t+18. Its positian at time t = 0 IS S© =4 and its…

A: This question is related to integration, we will solve it using given information.

Q: Given f(a) = 1- 홀 (3 + 4a) + 용(3+ 4z)2 - 꿈 (3+ 42)3 then f'(x) = 27 (3 + 4x) 8. 흥(3+ 4z) + (3+ 4z)2…

A: topic - derivative of a function

Q: of Find (1.-7) if f(x.y) = 2x2 + 4xy - 5y? + 4x - 9y - 9. dx of (1, -7)-O (Simplify your answer.)

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Q: 3) roțațion 90° counterclockwise about the origin

A: We know that,  90° counterclockwise rotation: (x,y) becomes        (-y,x)

Q: Using the substitution z=Vx+2, the integral xyx+2 dr is equivalent to (A) | 222(z2- 2) dz .7 (в |…

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Q: dy = (Type an integer or a simplified fraction.)

A: Topic:- double integration

Q: Use the graph below to find exact values of the indicated derivatives, or state that they do not…

A: Topic:- function and application of derivatives

Q: Find parametric equations of the line through (-1,0,1) that is parallel to 2i – 6 j+ k. -

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Q: The number of bacteria in a culture is increasing according to the law of exponential growth. The…

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Q: 12 dx Evaluate the integral: (9+3x)3 63 1. 36 1. 99 None of these 72

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Q: Q2: Apply the differentiation rules to find the derivatives of: 3x- sin x (a) y=e° Chain rule (b)…

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…