Q3/ A. For the following function f(x). Find: f(x) = x² + 1 i. ii. iii. The slope of the f(x) by using definition. An equation for the line tangent. At what points the f(x) has a horizontal tangent.

Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x sin²x (2) lim, o…

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Q: Use the tabulated values of f to evaluate the left and right Riemann sums for n = 10 over the…

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Q: 34. dx = x³+4x² + 5x - 1 is given. What is ƒ(1)? A.-7 B.3 C.-2 D. 16 35. Evaluate the integral f(x²…

A: 34) The integration of the integral is f(x)/x2=x3+4x2+5x-1.  35) The given integral is…

Q: (C): Solve the following equations:- (1) sin 2x + 2 sin² = 1 (2) sech x - 4 tanh x = 1

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Q: Find dy x 3 In (x - y) = xy + y²

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Q: Q2: Solve the following integrals: (1) 7x²+14x+15 (x²+3)(x+7) dx ; (2) sinx+cos x sin³ x cos³ x

A: Since multiple questions are asked, I am answering first question

Q: Match the graph of the surface with one of the contour maps. f(x, y) = e¹-x² - y² O O X x

A: Given that       f(x,y) = e1-x^2-y^2

Q: Use the method of reduction of order to find a second solution of the differential equation t²y" —…

A: The differential equation is given by,  t2 y'' - 4t y' + 6y = 0  Given,    y1 (t) = t2

Q: Suppose r' (t) = (cos(t), et, 2t) and r(0) = (1, 0, 3). Find r(t).

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Q: A rectangular box with an open top has a length of x feet, a width of y feet, and a height of z…

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Q: (A): Solve the following linear equations by Cramer's rule: x + y + 2z = 1 2x-y-z = 0 x +2y-z = 4

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Q: Q5: Find for the following functions: (1) In(x - y) = xy + y³ (2)y=tan³ √/cot(7x); (4) y = x sinh…

A: Solution is given below:

Q: Evaluate the following limit. sin xy + cos xy 2y lim (x,y) →(0,)

A: The objective is to evaluate the limit.

Q: Suppose that f is integrable on [-4, 7]. If the average of f on the interval [-4, 7] is 4.25, fin 4…

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Q: Rewrite the expression In 3 + 5 ln x + 6 ln(x² + 4) as a single logarithm In A. Then the function A…

A: We know the property of logarithm that  ln(a)+ln(b)= ln(ab)  ...(1)  And,  pln(x)= lnxp .....(2)…

Q: a Use possible symmetry of the graph to determine whether it is the graph of an even function, an…

A: Note : As per our company guidelines we are supposed to answer only one question. Kindly post other…

Q: cise (a) e volume of the solid formed by revolving the region about the x-axis 01 he region is…

A: To find the volume of solid revolving around x axis using disk method

Q: A. Find the following limits. Answer four only. x-¹-1 i. ii. iii. lim- X-1 X-1 lim 4x-x² X-4 2-√√x…

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Q: Discuss the continuity of the function. f(x, y, z)= sin(z) ex + ex continuous except at (0, 0, 0)…

A: Our Aim is to discuss the continuity of the function given below:-f(x,y,z)=sin (z)ex+ey -(i)

Q: 2x+3 (2x² + 6x − 1) b. f 1)s dx

A: B only Integrals by Substitutions

Q: Question 3 Find the Wronskian of two solutions of the differential equation t²y" — t(t − 2)y' + (t −…

A: To find out the wronskian without solving.

Q: Evaluate the following integral. π 2 7y sin y s s dx dy 0 0

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Q: (B): Find the tangent equation to the curve y = sin²x at point x =

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Q: Given that 2 ≤ f(x) ≤ 4 for 4 ≤ x ≤ 5, estimate the value of 5 0³/ [ f(x)dx 5 [²₁ <5 f(x)dx

A: Given 2≤f(x)≤44≤x≤5To find range of∫45f(x)dx

Q: dy dx Q5: Find for the following functions: (2) y = tan³√√cot(7x);

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Q: Let g(x) = = f(1) dt, where f is the function whose graph is shown below. At what value of x does…

A: Given: gx = ∫0xftdt Using Leibniz integral rule, we get g'x = ddxxfx -  ddx0f0 g'x = fx

Q: The region bounded by x = 1 - y¹, x = 0 is rotate about the line y = -5. The volume of the resulting…

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Q: Q4: Answer two only: 4 2 2 1 -2 -1 1 Find AB and AC. (A): If A = 0; 2 3 1 B= 2 -2 -2 and -1 2 1 3 C…

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Q: Which of the following functions describes the graph of g(x)? -10- + O g(x)= O g(x)= (2) 2²-8 2²-8…

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Q: sin 8 cose √cos²0-9 S do

A: Our Aim is to evaluate the integral given below:-∫sin θcos θcos2 θ-9dθ -(i)

Q: Use the comparison theorem to compare Enter your answer using either ≤ or >. F = = [₁* (√x + I + 2)…

A: We will use comparison theorem to compare the given two Integrals.

Q: 4. A one-way road has an overpass in the form of a semi-ellipse, 15 feet high at the center, 40 feet…

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Q: of x³ (4+x²)² dx ; Use rationalizing substitution

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Q: Question 1 a) Find the value(s) of y such that the vectors U₁ = and u₂ = are parallel. b) Find the…

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Q: y"+y=t y'(0) = -2 y(0) = 1

A: The differential equation is given by      y'' + y = tThe auxiliary equation of the corresponding…

Q: Find all critical points of the following function. f(x,y) = 10x²-5y²

A: Please see the below picture for detailed solution.

Q: What is the distance between two points (3,-1) and (-2,-5). 3

A: Given that the two points (3,-1) and (-2,-5)  To find the distance between the two points.

Q: -9 (x-1) 8. √x dx

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Q: Q2/A Cylindrical tank with radius of (3 m) and height of (10 m) has initially filled with water. In…

A: Please see the below picture for detailed solution.

Q: dw (C): If w = tan x and x = 4t³ + t ; Find dt

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Q: 16. (yety-1/y) dx + (xey + x/y²) dy = 0

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Q: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: 15,0-20³²4 2. 3. चं 5. T cos 2x dx sin(³) cos²( :-) / dx 2x - 1 4x dx dx 6. 7. [² (x² + 0²³) dx (x -…

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Q: Q1: Answer two only (A): Solve the following linear equations by Cramer's rule: x+y+2z=1 2x-y-z=0 x…

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Q: Q5: Find dy dx (1) In(x - y) = xy + y³; for the following functions: (2) y = tan³√/cot(7x);

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Q: 1. (1) E (14) (1) Choose the correct option (Multiple Choice Questions): Which of the following is a…

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

Q: Q5: Find for the following functions: dx (1) In (x - y) = xy + y³ ; (2) y = tan³√/cot(7x);

A: Given :lnx-y=xy+y3y=tan3cot7x

Q: The half-life of Strontium-90 is 28.79 years. If a sample contains 490 mg, how many mg will remain…

A: Given half life is 28.79 years Initial mass =490mg To calculate mass after 180 years.

Q: Q5: Find d for the following functions: dx (1) In(x - y) = xy + y³ ; (2) y =

A: As per Bartleby guidelines rule I am answering only first question as other questions are not the…