- Evaluate sin 0 if cos 0 = 2/5 and 0 is in quadrant I. Evaluate cos 0 if sin 0 = -1/4 and 0 is in quadrant III.

Q: b) sin(xy) = sin(x) + sin(y)

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Q: Compute the partial derivatives: 5x dz dz

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Q: Match the point in polar coordinates with either A, B, C, or D on the graph.

A: The given polar coordinate -2,-π2

Q: What is the expanded formula for a family with 8 children? O a + 8ab+ 25 + 56ab + 80a b + 56a b +…

A: Consider a family with 8 children

Q: Question 2 ( Consider the initial-value problem y" + 4y = 5 sin 3t, y(0) = 0, y'(0) = 3. (a) Use the…

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Q: 8. Evaluate dx . 6x A) +C 6. D) -C B) +C 5x 7x7 O b C O d

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Q: Find the equation of the tangent line at the given point on the following curve. x* +y = 20. (2, –…

A: The given curve,    x2+y2=20, 2,-4

Q: əf. dy and In each of the following, find dx (n) f(x,y) = tan x tany %3D

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Q: LOSA ५.

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Q: Find the equation of the tangent line at the given value of x on the curve. 3 4 2y° + xy - y =…

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Q: f(x) = (6 – x) | g'(x) and h'(x). ) = the Product Rule to find the derivative of f(x). II

A: Topic:- derivatives

Q: Problem #2: Differentiate f(x) = [(4x* – 5)(3x² – 9x – 5)]° and solve f'(2). (5 pts.) Solution:…

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Q: Find the area of the triangle. Round to the nearest tenth. S 16 km 66° R 7.8 km 62.6 km2 11 km2 O 57…

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Q: P3: tan 3x sec 3x dx

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Q: Match equation question type with a graph I- A V%3D (2 - B) (z - A) (z- A) (z - B) %3D

A: Graph: 1: a figure (such as a sequence of one or more points, lines, line segments, curves, or…

Q: Ssin ³xcos³xdx

A:

Q: Use the limit comparison test to determine whether each of the following series converges or…

A: Topic:- sequence and series

Q: 3 5) lim(1+ 2x)x x→0 6) lim(3* – 1)*

A: Given query is to find the limit of the expression.

Q: ) Use implicit differentiation to find dz/dx and dz/dy for x² + y² + z² = 3xyz.

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Q: Find the equation of the tangent line at the given value of x on the curve. y + xy? - 5 =x+3y; x= 3…

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Q: Compute the partial derivative: f(x, y) = sin (a- 6y) f,(0, T) =

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Q: 2. The Auxiliary Equation : (4D* – 4D' – 23D² +12D+36)y = 0

A: Given: 4D4-4D3-23D2+12D+36y=0 So, 4m4-4m3-23m2+12m+36=0

Q: 13. Let f(x)= x +3x-9x-13. (a) Find the intervals where f(x) id increasing and decreasing; (b) Find…

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

A: Here we have to find relative maximum ,mininmum points and saddle points.

Q: Let D be the solid unit cube: 0 < x < 1, 0 <y< 1, 0 < : < 1. Let S be the closed surface boundary…

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Q: At what point on the line y = b does the line segment from (0,0) to ( a,0) subtend the greatest…

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Q: The derivative of a function F(x) is f(x)=4x3. If F(x)= 10, what is the constant of integration? a.…

A: Topic:- function And its antiderivative

Q: The position of a particle on the x-axis is given by (t) = t – 4t + 3. At what time is the…

A: solution:-position of particle is given byx(t)=t2-4t+3velocity, v(t)=ddtx(t)…

Q: Exercise 1. Find the following limits sin 3x+ tan 2x2 2x? + x tan 2x 1) lim 2) lim 5x +x tan 2x 3)…

A: Use limit property

Q: Determine if the infinite series is convergent or divergent. State the test that you're using and…

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Q: Su(u² + 3) du

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Q: Sx² sec2 x³ dx

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Q: In the differential equation (2x+3y-5)dx+(3x- y-2)dy=0, the lines 2x+3y-5 =0 and 3x- y-2 =0…

A: This question can be solved using the concept of solving two linear equation.

Q: Problem 4 Solve x Iпy lnx dy + dx

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Q: dy Find for y = tan-(3z) de Ans=

A: A detailed solution is given below.

Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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Q: dx Given dt 1 and y = 6. Find for x2 + y² = 100 dt O A. 3 4 O B. 3 4 3

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Q: Solve the triangle. Round your answer to the nearest tenth. mLA = 46°, c = 9, a = 8 mLB = 8°, m2C =…

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Q: Convert to degrees. Convert 130° to radians.

A: Given query is to convert indicated angles

Q: 10. S V9x2 + 64 11. ( sech?(In x) 12. S cosh(5x – 7) dx

A: Given

Q: In 2 e2x dx V1+ ex

A:

Q: Let f(æ) = tan-(sin(7«)) f'(x) =

A: Let's find.

Q: Differentiate the following function. r(1) = (e!2e!-4e) %3D r(1)=

A: We can solve as follows

Q: The graph of a function is given. Use the graph to find the value does not exist. ta fx) b. f(1) -21

A: solution:-(a)According to the given graph of function f(x)limx→1 f(x)=-3becauseleft hand limit…

Q: Solve the triangle. Round your answer to the nearest tenth. 26 42 В 17 mLB 3D 112°, а 3D 25.9, b —…

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Q: 3 of 7 f(x) = {x - 2, *5 3 x+4, %3D is continuous everywhere. x > 3 O false O true

A: Given query is to find function continue or not

Q: Suppose the position of an object moving horizontally after t seconds is given by the following…

A: Given equation is quadratic so accordingly draw the graph and then solve .

Q: 1 ): The vectors 2 and form a basis the vector space R'. Select one: O True O False

A: Here we state whether it is true or false.

Q: y = x' cosx

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Q: 1 What is the instantaneous rate of change of Y= at x = 2? - o-1 4 O none of these -1 -1

A: