Evaluate the sum 50 Σ(2 · k + 5) = k=1 50 Σ5₁(2. k+5). k=1

Q: Question 1. Find the solution of the following differential equations (i) cos²x sin x + (cos³x)y = 1

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Q: Which among the choices is the same as the differential equation dP -= P(C₁-C₂P)? dt

A: Which of the following choices is the same as the differential equation.

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/2 when x = -1 and y =…

A: We have to find the value of c.

Q: Solve for the value of constant C in the equation: (2x + 3)y' = y + (2x + 3)¹/² when x = -1 and y =…

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Q: (g) Differentiate g(x) = V/1-2²-cos¹ (√2) COS (h) Find (1) Find do [sec (arctan (62))] de sin-¹(cos…

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Q: In 1997, there were 41,512 shopping centers in a certain country. In 2007, there were 48,662. (a)…

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Q: In 2004, an art collector paid $59,886,000 for a particular painting. The same painting sold for…

A: To find out the exponential growth rate and also the exponential growth function.

Q: Which among the choices is the same as the differential equation dP dt = = P(C₁-C₂P)?

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Q: 8. Find the limit of f(x) = lim f(x)= 4- 818 (Type a simplified fraction.) lim f(x) = 8118 (Type a…

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Q: The integrating factor (IF) of the equation y' - 2ycot2x OA sin2x OB. cot2x OC.Lnsin2x OD. CsC2x OE.…

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Q: Find the general solution of the differential equation y" + (wo)²y = cos(wt), w² ‡ (wo)². NOTE: Use…

A: Solution: Given data, y"+(w0)2y=cos(wt) Lets compose the auxiliary equation m2 + w02  =0 m1 = iw0 m2…

Q: Show that__(csc(x)) = -csc(x) cot(x). dx

A: We have to show that ddxcscx=-cscx cotx

Q: Suppose that F(x) = √ (t +)dt where x < 0. Using the Fundamental Theorems of -4 Calculus, find the…

A: Given ; F(x)= integration of (t+1/t), t from -1/x to x2.

Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

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Q: Evaluate 5 [C%² 0 5y 2e² dx dy

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Q: If f(x) f'(x) = f'(1) = 2 sin x 3 + cos x 2(1+3 cos(x)) (3 + cos(x))² then

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Q: A solid lies between planes perpendicular to the y-axis at y = 0 and y = 1. The cross-sections…

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Q: Homework 3.2 For #1-6, differentiate. 1.y = xe* ex 2. y = ² x+2 3. f(x) = 3x+2 x²+5 x²-4 4.…

A: We can find the derivative of the given functions by using the following formulas.

Q: 4. Let sin² x + cos² y = x² + y². Find y' by using implicit differentiation. ។

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Q: 7x - 4 3 – – 4x 4x² dx

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Q: Which of the following is TRUE about the differential equation x- dx O A. The equation is…

A: We have to find form of given differential equation.

Q: -22 - x2, find f(x), f(x), f(x), and f(4)(x). " (x) 70 = aph f, f', f", and f" on a common screen. y…

A: Given query is to find indicated derivatives.

Q: O D. dependent variable = y, second order, first degree, not linear

A: The given differential equation

Q: dy Solve for the value of C in the equation: + ycotx dx O A.-5 OB. 5 OC.-4 O D. 4 O E. None of the…

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Q: Question 27 The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy² + 2y)dx + (2y³ +…

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Q: lim h→0 f(−4+h)-f(−4) h

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Q: Solve for the value of C in the equation: (2xy4e³ + 2xy³ + y)dx + (x²yªe¥ − x²y² – 3x)dy = 0 when…

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Q: ple of gas is compressed at a constant temperature, the pressure P of the gas is inversely…

A: Pressure is inversely proportional to volume , take k as constant   for P = 50 kpa , and V = 0.103…

Q: Which of the following is a non-homogeneous function? tan³y/x xLnx − xLny - xy + y² (y² + v²)3/2 43…

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Q: Which of the following equations can be made into a linear diff O A. (x² + xy)dy - (lnx - Iny)dx = 0…

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Q: Determine the solution of the differential equation: (3tanx-2cosy)sec²x dx + tan x siny dy = 0

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the present value of $4000 payable at the end of 4 years, if money may be invested at 8% with…

A: The amount $4000 payable at the end of 4 years, the money invested at 8% with interest compounded…

Q: Find the area bounded by the curves x y = 8 (in green), y blue) and the line 3y sliced pizza? 2 =…

A: Let's find area of the sliced pizza.

Q: . If (OM-ON) / - - - O A. B. O E. "Q y5 -5 then what is the integrating factor? None of the Choices

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Q: Find all values of n such that y = x" satisfies x²y" - 20y = 0

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Q: In Exercises , say whether the function is even, odd, or neither.Give reasons for your answer.51.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Use the Gauss-Jordan method to solve each system of equations. 4x + 4y-4z= 36 2xy + z = -3 x - 4y +…

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Q: f(x) = ln(x), ro= 100, and 2₁ = 105.

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Q: Which of the following is a non-homogeneous function? tan³y/x OxLnx-xLny O x³ − xy + y² (y² + v²)³/2…

A: homogenous function is f( tx,ty ) = t^n f(x,y) option a) f(x,y) = tan (3y/x) now,…

Q: The length of a stalactite (in mm) has been measured at the beginning of every fourth year since the…

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Q: Eliminate the arbitrary constants of y=c₁e*+cx*— sin3x

A: We use differentiation to Eliminate the arbitrary constant, we differentiate the given equation as…

Q: The rate of change of the variable y in terms of another variable t is equal to the expression 5t4 -…

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Q: Which of the following equations is NOT a variable separable differential equation? A. 2xydx + (x² +…

A: A Separable differential equation is any equation that can be written in the form of dydx =…

Q: Find the term indicated in the expansion (2x + y)6; third term.

A: Given: The given expression is: (2x + y)6 Formula Used: Binomial expansion: a+bn = C0nanb0 +…

Q: (g) Differentiate g(x) = V/1-x².cos-¹ (√) (h) Find d de (i) Find [sec (arctan (02))] d [sin -¹(cos…

A: In the given problem, three differentiation are provided. We have to differentiate each. To get the…

Q: Find the derivative of the function. F'(x) F(x) = (4x + 8)³(x² - 5x + 8)4

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Q: Which of the following equations is NOT a variable separable differential equation? A 2xydx + (x² +…

A: See this solution in below.

Q: Find f'(x) and simplify. f(x) = 8x*(x³ -9) 3 Which of the following shows the correct application of…

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Q: 5 (lx-21-4) dx

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Q: 7. Find (a) the slope of the c y=9x² -1; P(4,143) (a) The slope of the curve (Type an integer or a…

A: solution:-y=9x2-1slope= dydx=ddx9x2-1=18x(a)slope of tangent at point P(4, 143)slope = 18(4)=72