Q4 Evaluate: f(1- cos²4x) sin4x dx.

Q: For which values of a and b E R is the following piecewise function continuous on R? (sin(2x) + a x…

A: for piece wise function  continuty condition is  limx→0- f(x) =limx→0f(x) = limx→0+ f(x)   now…

Q: Express as a single logarithm and, if possible, simplify. 1 log b + 3 log c 2 1 log b +3 log c= 2…

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Q: A particle start from the point (4,4) and it's coordinates change by the increment AY=5 and AX= -8…

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Q: Find the general solution of the given differential equation. 2 dy dx - + 6y = 3 y(x) = Give the…

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Q: Find the solution of the given initial value problem in explicit form. 1 y' = (1 – 3x)y², y(0) = 8…

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Q: Find the derivative of the function. g(x) = (sech(7x))² g'(x) =

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Q: Find the inverse function of f(x) = Specify the domain for f-¹(x) f-1(2) = = 2-9 Domain of f¹(x)…

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Q: Solve the given differential equation by separation of variables. dy dx x√ 1 - y² y = =

A: Solving the problem by finding the value of the problem.

Q: Find the general solution of the given differential equation, and use it to determine how solutions…

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Q: dy 2 +6y=3 dx y(x) = Give the largest interval I over which the general solution is defined. (Think…

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Q: First use appropriate properties of logarithms to rewrite f(x), and then find f'(x). f(x) = 2 In…

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Q: If z = y¹ - 4y³ + 4y² - 1, then the set of values of y for which z' equals 0 is A. {0, 1, 2} B.…

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Q: 4) A coin is dropped from a height of 960 feet. The height, s (measured in feet), at time, t…

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Q: state the order of the given ordinary differential equation. Determine whether the equation is…

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Q: a. Find the linear approximation for the following function at the given point. b. Use part (a) to…

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Q: At what points of R² is the following function continuous? 17 f(x, y) = x5 (y² +81)

A: Solve the following

Q: Q1/ Find -1 s² (s+1)(S-1)²

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Q: The position vector r describes the path of an object moving in space. Position Vector Time r(t) =…

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Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

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

Q: A) Find the Laplace transform of (2 03

A: We have to solve given Questions.

Q: If possible, find the absolute maximum and minimum values of the following function on the set R.…

A: Given function is fx,y=3x2-3y2+1 and region is R=x,y:x2+y2≤1

Q: (b) y = e, y = ²x, x=0, x= ln 2 1 (c) x = =, x = 0, y = 1, y = e Y (d) y = 5x - x², y = x (e) y =…

A: Using vertical strip

Q: Find the length of the curve. r(t) = √√2ti + etj+ek, 0≤t≤7

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Q: A/ By using Linear equation solve the first order differential uation y' + sec(x)y= cos(x)

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Q: Solve the given differential equation by using an appropriate substitution. The DE is homogeneous.…

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Q: Initially 100 milligrams of a radioactive substance was present. After 6 hours the mass had…

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Q: Find the equation of the plane tangent to the following surface at the given points. x² +…

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Q: The time in seconds, t, it takes for a specific object being dropped from a particular height in…

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Q: Q4\ Solve by Gaussian elimination x-4y-2z = 21 2x+y+2z = 3 3x+2y-2=-2

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Q: 1. Evalaute lim ƒ(x), lim ƒ(x), lim f(x) for I-3+ 2-3- 1-3 f(x)= { = −x+4 x − 3 x 3

A: Topic = Limits As per guidelines , At a time only one question with three sub-parts can be answered…

Q: Find the solution of the given initial value problem. π ty' + 2y sint, y = 1, t > 0 Y || =

A: In this question, we want to find the solution of the given first order non-homogeneous linear…

Q: Z Z 2 J 0 iei(n+1)0 de

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Q: Q1: Find the general solution of the following first order D.Es? (Answer two only) CELE MAI ) c)…

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Q: 3. Determine whether the function is continuous at r = 5. 2²-42-5 2-5 x 5 D

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Q: Find the velocity and position vectors of a particle that has the given acceleration and the given…

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

Q: Given the graph of fx), determine the range of f(x) • 8 -10-9-8-7-6-5 OR O(-1) (1.) O(-2) u (2) O(1)…

A: Range of an inverse function is the domain of the orginal function.

Q: 8. Find the area bounded by y=ex, y=x² and x=2. a. 3.1 u² b. 4.1 u² c. 5.1 u² d. 6.1 u²

A: Here we have to find the area bounded by the given curves.

Q: 16. A cup like object is made by rotating the area between y = 2x² and y = x+1 with x> 0 around the…

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Q: What is the slope of the tangent line to the graph of the solution of y' = 6√y + 7x³ that passes…

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Q: IF y = u² + 3u² & u = 2x Find d dx 8x(8x^2+3) (64x^3+30x) O 8x(8x^3+3) O 8x(8x^2-3) O

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Q: Laplas Inv Q1/ Find -1 s² (s+1)(S-1)²

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Q: -1/3 4/3 (4) Find t(n) for the function t(n) = 3n +4n (4) (n) =

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Q: Find an explicit solution of the given initial-value problem. √2 √1-y² dx - √1-x² dy = 0, y(0) = 2 y…

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Q: TU The result of f fysinxdxdy = O 1 O -1 O 1.5 O -1.5

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Q: Graph several level curves of the following function using the given window. Label at least two…

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Q: Find the solution of the given initial value problem. T ty' + 2y = sint, y = 3, t > 0 2 Y ||

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Q: Find g'(x) if g(x) = 6xex g'(x) =

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Q: Solve the given differential equation by finding, as in Example 4 from Section 2.4, an appropriate…

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Q: The following limit gives the derivative of a function f(x) at a point xo: lim h→0 (2+h)³-8 h -8)…

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Q: To find the volume formed by the function z=f(x, y) = x²y over the triangular region bounded by the…

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