Evaluate the indefinite integral. (Use C for the constant of integration.) xV7 - x2 dx

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Q: 21. Determine the general antiderivative of f(x) = 4x 4x4 + 9 2x2 a. 2 cosh +C 3 22 + C c. 2 sinh¯ -...

A: As per our guideline we are supposed to be answer only one question you can repost other question in...

Q: Find the solution of the given initial value problem. cos t y + y(m) = 0, t>0 y(t) =

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Q: uate lim t→+∞\ 3t2 + 2

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Q: Find the inflection points of each of the given curve.  3y = x3 + 3x2 – 9x + 3

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Q: 1 2x-9 13 Evaluate lim 1 x→-2 - 2x+8 4

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Q: Computational: (1) The concentration C of a certain chemical after t seconds of an autocatalytic rea...

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Q: ax +1) dx

A: we want to find the value of integral ∫ax2a(x2a+1)3xdx

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Q: Water is poured into a conical container at the rate of 10cm³/sec. The cone points directly down, an...

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Q: Find the inflection points of each of the given curve.  4y = 3x4 – 16x3 + 24x2

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Q: For the next five questions, consider the following differential equation: (7 + zy')dr + (5y – ry + ...

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Q: 1. x cot2 xdx X CO

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Q: dy Which of the following is the general solution to the differential equation dx e x+ In x = C y ex...

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Q: Find the length of the arc of the curve x = t, y= t° between the points for which t = 0 and t = 2. %...

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Q: Evaluate the following integrals. 1. sec-a dæ cos Va dx Væ csc /æ 2. x2 dx - 3.

A: Integration by parts

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Q: Evaluate the following integrals. 1. 4x sec .3 -1 x dx

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Q: Find the gradient of f (x,y,z) = e^(x+y) cos(z) + (y+1)tan^(-1) (x) at the pint (0,0, pi/6) Alternat...

A: The function is given by fx, y, z = ex+ycosz+y+1tan-1x The point is x, y, z = 0, 0, π6 To evaluate: ...

Q: Find the derivative of: y=x^(7sin(x)). (x>0).

A: Multiplication rule of derivative is used.

Q: There is a jump discontinuity at x = 1 and lim f(x) = 1

A: At X=1, there is a jump discontinuity.   limx→1- f(x) = 1.As function f(x) approaches towards 1 from...

Q: What is the particular solution to the differential equation x(x³ – xy² + 2y³)dy – y(x³ + 2y³)dx = 0...

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Q: Make 3 unique examples of domain and range in real life scenarios. Please highlight the domain and r...

A: To write: 3 unique examples of domain and range in real life scenarios.    

Q: Find the radius of convergence and the interval of convergence. 2k+1 k2 + 81 k=1 Radius of convergen...

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Q: Find the value or values of x for which the curve of the following functions has a point of inflecti...

A: Given, y = (x – 1)4 (x – 6) We can find inflection point by finding second derivative and equating i...

Q: An object moves along the a-axis, its position at each time t > 0 is given by æ(t) = t" 3 4 +t. Dete...

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Q: Eliminate c, x'y =1+ cx (2+x3y)dx + xdy = 0 B (1+x?y)dx + x³dy = 0 © (1+x?y)dx + x²dy = 0 D (1+x3y)d...

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Q: Find the direction cosines of the vector v = (2, –4, 4) %3D

A: The given vector v→=2,-4,4

Q: .3 dx

A: Definite and indefinite integral 

Q: Solve the following problem related to function. (Show your solution) 4. What is the equation of the...

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Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

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Q: Since (k + 1)!/3k+1 lim k +1 lim k→+∞ 3 +00, %3D k→+0 k!/3k k! the series (converges/diverges/inconc...

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Q: 7. Determine which of these positive integers are a) 1,5,7,11,13,17,19,21, 23,25, 29,31 b) 1,5, 7,11...

A: We know that  Two numbers are said to be relatively prime if their greatest common divisor is one. F...

Q: The cost of producing an ordinary cylindrical tin can is determined by the materials used for the wa...

A: Given:       Volume =1000 cm3       Volume of cylindrical tin V=πr2h      then,            πr2h=1000...

Q: 3. Express the quadratic function g(x)=-4x² +4x+5 in the form a(x-h)' +k by completing the square, a...

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Q: sinr f(x)=(x)'

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Q: 4. Given that r(t) = cos ti + sin tj + In cos tk Find the curvature k and vec- tors T, N, B at the g...

A: Find curvature at t=1

Q: 2-Vn n=1

A: Here, the given series is: ∑n=1∞2-n=∑n=1∞12n=∑n=1∞12n2 which is a positive term series for all n.

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Q: The number of bacteria "N" present in a culture increases at a rate proportional to the number prese...

A: Topic:- function

Q: Find the area of the cardioid r=2(1+cosθ). a. 2π b. 4π c. 5π d. 6π e. none of the above

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Q: dy Write down a differential equation of the form dt = ay + b whose all other solutions diverge from...

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Q: All edges of a cube are expanding at a rate of 6 centimeters per minute. Draw an accurate  picture t...

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Q: Evaluate the following limits. (b) lim v9r² – 5x + 3x

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Q: Let F(x,y,z) = (y,x²,zy) where C:R(t) = (cost,sin t , 3t) and t e [0,2]. Evaluate %3D %3D •dR

A: We have to find value of given Integral.

Q: 1. If time, t, is in hours and concentration, C, is in ng/ml, the drug concentration curve for a dru...

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Q: Write this term in mathematic language: bcos(ax)^2, a-(sort(5)-1)/2

A: Let's find. 

Q: -x' + 2 Find the slope of the secant line between x = -3 and x = 3 for the function f(x) = (Enter yo...

A: Given that a function f(x)= (-x3+2)/(2x-2). And we find secant slope of line between x=-3 and x=3 fo...

Q: 3. y'(x'y-2)dx+x(x*y' + 2y° - x)dy = 0 : y(1) = 1

A: We have to find the particular solution. 

Q: This case study is about fitting data to various exponential-type functions. (Chapter 5) A commercia...

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