Write Tif the statement is true, or F if it is false. Write your answers on the blanks. dx x +C 3 2. 45x 5- -dx = -5x +C 4 12x -4x + dx =-x'+2x +C 3.

Q: The limit below represents the derivative of some function f(x) at some number a. 3(3 + h) - 243 lim…

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Q: Consider the parametric curve defined by 1=3+5t and y=1+3 Over which values of doesthe curve has a…

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Q: Find the points on the curve y= (x-1)(x -4) where the tangent line is parallel to y= -4x, O (3, 10)…

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Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: 0.125 А. f(8t) dt | 0. 0.25 B. f(1 – 4t) dt = 2.5 c. f(5 – 2t) dt =

A: Given that,

Q: applying substitution méthöd: sqns -48

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Q: Q2) Convert the polar function r tan20 to cartesian.

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Q: Q2) Solve the D.E x²dy + (3xy- 1)dx 0

A: Let's find.

Q: Let a = 2i - 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8

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Q: Q5) Find volume of body bounded by z2 + y2 + x2 = 4.

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Q: Evaluate triple integral f, SE Lx? - y?)dz dy dx.

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Q: All edges of a cube are expanding at a rate of 8 centimeters per second. (a) How fast is the surface…

A: All edges of a cube are expanding at a rate of 8 centimeters per second.a To determine how fast is…

Q: Q3) Find the Area bounded by the curves x and x = 2y – y².

A: Topic = Area Area bounded by curves is 13.

Q: Since f'(c) f(1) – (0) f(1) – f(0) = 1, f(c) = 1. We therefore equate f'(x) to 1 and solve for x.…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = V9x2 + 16

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Q: Q3) Evaluate triple integral y(x2-y?)dz dx dy.

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Q: Evaluate: / y6 sech(e7hny) tanh (e 7Iny) dy A) -sech(y?) +C 7

A: We know that    elnx=  x we use above result to determine the integral

Q: Let a = 2i – 3j and b= 2j + 3k. Compute for the following: (a + b) · (a – b) None of the choices -8…

A: Here we have to find the dot product.

Q: Q2) Solve the D.E xy(x? + 1)dy - (y? + 1)dx = 0 %3D

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Q: Use the appropriate Product Rule to evaluate the derivative, where ri(t) = (9t, -10, -t°),r2(t) =…

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Q: y = Vx* X

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Q: Find volume of body bounded by z 0 from below and z = 4 - y from above inside y = x2 ,y = 4 .

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Q: Use the first principles definition of the derivative to find f"(2) where Ax) = O a) 0.125 b) 4 c)…

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Q: The shaded region R is bounded by the lines x = 0, y = 0, and the curve y = x² – 2x + 2 as shown in…

A: Here, the volume is: V=∫03π(y)2dx =π∫03x2-2x+22dx=π∫03(x-1)2+12dx

Q: Obtain the general solution unless otherwise instructed A. LINEAR EQUATIONS WITH CONSTANT…

A: Note:- These are multiple questions and according to our company guideline we can do maximum one…

Q: Consider the parametric curve defined by x=3+5t and y=1+3t Over which values of , does the curve has…

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Q: Question 18 Consider Evaluate O (9x4+6x)e (x3+y2) O (3x²+6x)e «³+y?) O (6x²+ 3x)e «³+y?) O (6r*+9x)e…

A: Topic = Derivative

Q: (b) Repeat part (a) using 3 subintervals and the velocity at the midpoint of each subinterval. mi

A: answer is in next step

Q: Find the derivative of f(x)= (In x O a. 6x(In x) O b. 24(In xỷ c. 24 In x O d. 12(In x)

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Q: Problem 2: Use the First Fundamental Theorem of Calculus to answer the ff. If F(x) = tvt +1 dt,…

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Q: Use cylindrical shells to find the volume of the solid generated when the shaded region is revolved…

A: Here, the volume formula is given by: V=∫012πy(g(y))dy=2π∫01y13y-13y2dy

Q: write the equation of a parabola whose directrix is x = 5.75 and has a focus at (12.25, 5).

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Q: (a) Show that the integral test applies, and use the integral test to determine whether the series…

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Q: Check the continuity of the function f(x). Explain why f(x) is continuous or not. x+1 =,x x2X > 1

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Q: 8. (5x'-4x +8x) dx

A: Topic = Integration As per guidelines , At a time only one question can be answered out of different…

Q: Find the value of the derivative (if it exists) at the indicated extremum. f(x) - - 3rVx+ 2 10 4. -…

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Q: Q3) Evaluate triple integral Lyx -y)dz dy dx.

A: Topic = Integration

Q: EValuate J s 2'as O a. 2*(sln2 – 1) (In2)2 O b.2(sln2 - 1) (In2)2 O C. 25 sp.7s (1 – Zu). + 1) In2 O…

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Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: .4 4-y Q3) Evaluate triple integral , S S dz dy dx.

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Q: Q2) Convert the polar functionr tan20 to cartesian.

A: Here we have to convert the polar function r=tan(2θ) to Cartesian.

Q: Find the value of x such that x satisfies the mean-value theorem at the interval [0. 1] for the…

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Q: Is it a function? 4 12 yes or no -1 -3 -4 -5 -21 Explain. 1 -3 4 12 -2

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Q: If f(x) and g(x) are continuous functions and p(x) = f(x) × g(x) use the table below to evaluate…

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Q: Given Ax) = - 2 use the first principles definition to find f'(1).

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Q: Helene invests Php 5,000 in an investment that earns 6% per annum. How many complete years doe it…

A: Topic = Algebra

Q: Find the value of t for which 1 V3x+1 O none of the choices 6 O 3 O 5 O 4

A: Here, given that: ∫1t13x+1dx=43

Q: 3 -1 3 0 Given F = show that: 19. –F" = (-F)" 20. (F")" = F m 2.

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx 2 y =

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Q: 24. dx AX

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