dx √x²=2x+17 a) sinh xe ta 4 bì ninh XH + C 4 c) minh? X-1 2 d) none of the above

Q: If the tangent line to y = f(x) at (5, 2) passes through the point (0, 1), find f(5) and f'(5). f(5)…

A: Topic = Derivative f5=2f'5=15

Q: Evaluate: limt. +00 ln 5t 4t²

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Q: Which of the following is equivalent to the expression a) √√³² Ob)-20 h³ d) h² • ?

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Q: For the following exercises, draw the region bounded by the curves. Then, find the volume when the…

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Q: y = In x (x-5)ez-1

A:

Q: 16. True or False: (a). Every element in a cyclic group (G) is a generator of G. (b). A group (G, *)…

A:

Q: 1. n² Determine whether the series Σn=13n+1 ln(n+1) is convergent or divergent.

A:

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

A: The given differential equation,      2y'+y=7t2

Q: dx What is , where dy' x³ + y³ = 3xyusing differentiation? implicit dx dy y-x² y² +x dx y-x y²-x dy…

A:

Q: Identify ALL the Indeterminate forms involved and determine the limit of: limo+ (cos(x))"

A: See the answer below

Q: Q3/ Answer one from the following :- 1- Determine the general solution y(x) for the equation 2y" -…

A: Explanation of the answer is as follows

Q: Solve the differential equation where y = 8 when = 0. y + 3y x + 3 = (x+3)8

A:

Q: Evaluate S 2 dx √x4+25

A: ∫1au+b du = 1alnau+b+C

Q: Given the function z= f(x, y) = ln(x² + xy - y²), find the following: a) Find gradient at the point…

A: As per our guidelines we are supposed to answer only first three subparts of the question. Kindly…

Q: 28 Which one of the following is the co-ordinates of the y-intercept of the tangent line to the…

A:

Q: Which of the following corresponds to the limx→4 (¹2) w when evaluated? 0 4 2

A: Here is the solution:

Q: -0.5 1 100³S 1-=X² dx represents the area of a region bounded by 1 O a. the vertical lines x = +0.5,…

A:

Q: 3. 플 I sincy) y dydx

A:

Q: Let y = f(x), where f(x) = 7x³ + 3x. Find the differential of the function. dy = X

A: The differential of y is the derivative of the function times the differential of x,

Q: Find the limo (cos x) = Show your complete solutions. No shortcuts.

A: Given,  limx→0cos x1x2

Q: 2 dy 67 +13

A:

Q: ect the best technique to integrate each function. ® Na'da 5 dx 16 V √ √₂²³-11 ·@fe²√5 + ode x + 7…

A: The objective of the question is matching the given indefinite integral.

Q: (ii) Suppose z = f(x, y), where x = g(s, t), y = h(s, t), g(1,2) = 3, gs (1, 2) = −1, gt(1, 2) = 4,…

A:

Q: 2.) Determine whether the geometric series is convergent or divergent. If it is convergent, find its…

A:

Q: x-2x +x= 15; x (0) = 7, x (0) = -16

A:

Q: When is a function Fan antiderivative function f? of a if F(x) is continuous for all x in the domain…

A: Given , When function  F(x) is called an antiderivative of a function of f(x).

Q: Find the area of the triangle in IR³ that has vertices P₁= (1, 0, 1), P₂=(2, 3, 1) and Ps= (0, 2,…

A:

Q: Which one of the following is the domain D for f(x, y) = ln (2²-(y-2)²) ? Select one alternative:…

A: The given function: fx,y=lnx2-y-22.We need to find the domain.

Q: L’Hopital

A:

Q: Use the graph below to determine that slope of the secant line on f(x) from x-1 to x-3. 5 4 3 2 y =…

A: use the graph for finding the slope of the secant line.

Q: 9 At what point do the following lines in R³ intersect? h: (x, y, z)=(3, 1, 2) + s(1,0,2), SER 1₂:…

A: Let's find point of intersection.

Q: First verify that the given vectors are solutions of the given system. Then use the Wronskian to…

A: Concept: Wronskian method: W(x1(t), x2(t), . . . , xn(t)) =x1(t) x2(t) · · · xn(t) xx1'(t) x2'(t) ·…

Q: Determine whether the differential equation - (7x² − 2xy + 3) dx + (8y² − x² + 7) dy = 0 is exact.…

A:

Q: What is S (x² + 2x)² dx? + x³ + ³x² + C 4 S (x² + 2x)²dx = ¹x¹ + x³ + 4 f (x² + 2x)²dx = (x² + 2x)¹…

A: We know, ∫xndx= xn+1/(n+1)

Q: Sylvia had planned a shopping trip to the United States so she bought US$500 from a bank when the…

A: Concept: Sylvia has US$500 First, the exchange rate was US$0.7834 for C$1 Then the exchange rate…

Q: Consider a 3 by 3 matrix A, where a11, 022, 933 are all zero. Suppose |A|0, how many terms in the…

A: Follow the procedure given below.

Q: 11 Let A be a 3 x 3 matrix. Which of the following is not a valid row operation when row-reducing…

A: Here we have to choose the correct option.

Q: Tess tried to solve the differential equation = 2xy - 6x. This is her work: dy = 2xy - 6x dx dy Step…

A:

Q: dy Find by implicit differentiation. Then find the slope of the graph at the given point. dx 3x³y =…

A:

Q: (i) Find the linear approximation of the function f(x, y) = 1 - xy cos πy at (1, 1) and use it to…

A: Here, the given function is: f(x,y)=1-xycos πy To find the linear approximation of the function. For…

Q: What is the derivative of x² + y² = 9 using mplicit differentiation? dx = xy dy dx = -xy dy dx dy dx…

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

Q: 13. The graph of y = f(x) and y = g(x) are shown below. g(x) 6 (a) (b) f(x) 2 10 -2 Find h'(9) if…

A: Explained below

Q: • How. Find the lengths for the following curver.. 1= r = 1 + cosa

A: Explanation of the answer is as follows

Q: Identify and sketch the graph of y = r²+1 in R³.

A:

Q: The differential equation y""+ay""+by" + cy + dy = 0 6t has a solution y 2tet 6e sin(3t) for real…

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Q: The domain for the function y = all real numbers except 3 and 0 ○ {x/x > 3} O less than 3 except 0…

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Q: What limit law is used in the given below? lim (5x + 2) = lim (5x) + lim (2) x →1 x →1 x →1 Addition…

A: We have to choose the correct option from the given options according to the given information

Q: xy lim 2 (x,y) (0,0) x² + y²

A:

Q: Evaluate: lim, 0 sin 2t t³ (t-1)²

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Q: 7. Determine the dimensions of a rectangular box, open at the top, having a volume of 32 ft³, and…

A: Given :Volume = 32 ft3