If u = f(x), then f- dx ++2x+1 +C for some constant k. Compute kf(1).

Q: Solve the given differential equation by separation of variables. (e + 1)?e-Y dx + (e* + 1)Se-* dy =...

A: Given:- (ey +1)2 e-y dx +(ex +1)5 e-x dy=0 To find :- General equation of given differential equatio...

Q: The standard form of the first order linear differential equation x'y'+ry +2=0is

A: The standard form of a first-order linear differential equation is:

Q: the

A: We will find the derivative. 

Q: Consider the integral 2h* g(x) dx. There is a function g(x) such that when Inx the resulting integra...

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Q: Eliminate the parameter to find a Cartesian equation of the curve. 1 x(0) -cos 0 20 y(0) = 4 cos(20)...

A: (a)To determine: The cartesian equation by eliminating the parameter. (b) Range of x-values, express...

Q: Find the derivative of y with respect to v. y = In (cosh (2v)) – tanh? (2v) The derivative of y with...

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Q: Answer the questions for the function f(x) = 3x - 24x a. Find formulas for f'(x) and f"(x). f'(x) = ...

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Q: Evaluate f-4*3 dx In4 b,- -3in4 +C C. In 64 d. none of the above Evaluate f4x cosx dx a. sin x + C b...

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly re-post other...

Q: Given that the graph of f(x) passes through the point (5, 2) and that the slope of its tangent line ...

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Q: Evaluate the integral. 15e cos(2x) dx +C NOTE: Enter the exact answer.

A: This question is based on indefinite integral.

Q: k If u = f(x), then f dx x4+2x²+1 +C for some constant k . Compute kf(1). x2+1

A: topic - functions and indefinite integral

Q: 2. xdy+(y-xy +2)dx=0

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Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say ...

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Q: dx +x tan y= dy sec y 1+tan

A: The given differential equation is; dx/dy +xtany=secy/(1+tany)

Q: equations

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Q: 3T en: S 5x² cos 3x³dx. If u = 3x³, then the resulting integral is S f(u)du. Find f (").

A: Given query is to find the indicated function.

Q: Evaluate the integral. In(10 x 9) dx +C

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

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Q: S(z) = 64 –3 V/

A: f(x) =x964-x3We can rewrite the function as;f(x) = x9  164-x3f(x)=x9 (1641-x364)a=164,  r=x364   (Ge...

Q: Find the indefinite integral. (Use C for the constant of integration.) xp J xV81 - (In x)²

A: topic ,- indefinite integral

Q: Determine whether the series converges, and if so find its sum. If the series diverges, indicate tha...

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Q: Ec Find the general term of the sequence, starting with n = 1. Determine whether the sequence conver...

A: topic - sequence and series

Q: A set of data with a correlation coefficient of -0.15 has a a) strong negative linear correlation c)...

A: As we know It is a statistical measure of the strength of the relationship between the relative move...

Q: Given: S 5x² cos 3x³dx. If u = 3x³, then the resulting integral is S f(u)du. Find f (*):- ... 5/7 5/...

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Q: what is the range of h(x,y)=ln(x+y-5)

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Q: Find the exact value of the expression, if it is defined. (If an answer is undefined, enter UNDEFINE...

A: topic- trigonometric ratios

Q: Consider the expression ſ V4 – x² dx = F(x)+C. The expression %3D F(2) – F(-2) is equal to

A: Here we have to evaluate F(2)-F(-2)=? We have, ∫4-x2dx=F(x)+C

Q: Find the length of latus rectum of the curve x² – 6x + 12y – 51 = 0.  a. 12 b. 13 c. 14 d. 15

A: The given equation is;  x² – 6x + 12y – 51 = 0. 

Q: Obtain the general and particular solution 2. 2ydx = 3xdy

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Q: If g(x) f'(x) and if g(x) (cos x - x sin x)e*cosx, then f g(x) tan(f(x))dx is x cosx In(e*cosx) +€ s...

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Q: Use sigma notation to write the Maclaurin series for the function 5 In(1+x) Σ

A: To find: The Maclaurin series of the function f(x)=5ln(1+x). Concept used: The Maclaurin series is f...

Q: -1)k+12 11 17.-(6k – 7) Use the formula for the binomial series: (1+ x)" = m(m-1)2 t … + m(m-1)(m-k+...

A: Here, the given function is: f(x)=1+66 And, the given binomial expansion is: (1+x)m=1+mx+m(m-1)2!x2+...

Q: 1. If x - y = 25, then y" = c.) d.) - a.) b.) 2. If y = cos(3x+1), find y a.) 3 sin(3x+1) b.) -3 sin...

A: Authoring guideline: As per the authoring guidelines, we can solve only the first three parts. Repos...

Q: Evaluate the integral. x sec (3x) dx = +C

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Q: 7 sin(t) + tan(t). tan(t)

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Q: dx The integral S reduces to S k, where u = f(x) and for some constant k . Compute f(1). ex+1

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Q: Gravel is being dumped from a conveyor belt at a rate of 30 cubic feet per minute. It forms a pile i...

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Q: . 2:(y-x² }tx+dy=0

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Q: y" + y " +y' + y = 1

A: A differential equation is said to be linear if no terms in it are formed by multiplication of two t...

Q: Determine whether the series converges, and if so find its sum. 4k+2 7メー1 k=D1 1) This series can be...

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Q: du formula answer 24 +2 (2x-1)"(Ax + 2)""

A: Given: I=∫24x+22x-133x+23dx  ...1   We know that; The Product rule: f·g'=f'·g+f·g' The Power rule: ∫...

Q: Set up a definite integral with respect to x (dx) (set up only, do not evaluate the integral) to fin...

A: Question: Setup a definite integral with respect to x dx to find the area of the region enclosed by ...

Q: A function and its first and second derivatives are given. Use these to find each of the following. ...

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Q: *e「ス+

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Q: f(x) = 15- (3-t)(r - 8t + 7)

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Q: Find the differential equation whose solution is given by: y^2 = 4ax

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Q: (x – h)? + y? = r² O y " +(y')² + 1 = 0 O y" +(y')² = 0

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Q: Find the derivative of the function. f(z) = Vī – 8V7 f (x) 12r – 83x23

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Q: I. Identify the elements for the following set expressions given the sets below: (Explain your answe...

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Q: 9. Evaluate f(e* + 2*) dx a.) 2e* + +C In2 b.) er + 2ln* + C c.) e* ++c d) e* + 2ln x + C In2 10. Ev...

A: Evaluate integrate. And follow step 2nd .  According to guidelines we solve only first three parts.