15. What is the derivative of the function: F(x) = x cos(5x) F(x) = x cos(5x) F'(x) = (x) cos(5x)+(cos(5x)) (x) dx F'(x) = cos(5x) + [-sin(5x) (5)] (x) F'(x) = cos(5x) - 5x sin(5x)

Q: Evaluate the following integrals. 2. √x+ +5x² x4+5x³+20x+16 x(x²+4)² dx

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Q: The cos³dy is {A}-sin+sin³+C 3 3 3 4 {B} sin¹-sin³+ C 3 4 3 4y (C)-sin-sin³+C {D}sin+sin³+ C

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Q: 3. (2 + y² + xy2) dx + (x²y + y + 2xy)dy = 0

A: As per the guidelines I can solve only one question

Q: Evaluate the iterated integral. - y² I. L (x + y) dx dy

A: Take integration

Q: using an online graphing app, construct three graphs which lie on the interval (-8,8) choose three…

A: The given interval is -8, 8. We have to sketch three graphs on the interval. Let us take functions…

Q: [18x² √6x³ +5 dx 3 ○a. — (6׳ +5)³/4 + C b. (6x³ +54/5 + Oc.5(6x³+5)¹/5 + C d. 5 Od (6x³+5) ³/4 + C…

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Q: INSTRUCTION: Prove or disprove 1. 3x-5 = is bijective. 2x+1 Show that f: R-{-}→R-{} defined by f(x):

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Q: Comput: f dx 2+x

A: I am attaching image so that you understand each and every step.

Q: The cos³4 dy is {A}-sin+sin³¹+C 3 4y 4 3 3 {B}sin-sin³¹+ C 3 4 3 (c)-sin-sin³+C {D}sin+sin³+ C

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Q: v+4 dv v-2

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Q: 2 The √tan x secxdx is {A} tan³/2x-tan7/2x + C {B} tan³/2x + ² tan7/2x + C {C} tan5/²x + tan7/²x + C…

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Q: Given that f (t) = t³e²t sint, which process will yield the less complex and correct Laplace…

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Q: Determine whether the improper integral diverges or converges. 00 √x³²e-x dx O diverges Evaluate the…

A: To find the integral: ∫0∞x2e-xdx converges or diverges.

Q: 38. a10-49.5, a14 = -73.5

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Q: approximate with accuracy 10^3 to the solution of x³+x-4 = 0, lying in the interval [1,4].

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Q: Given sin(a)= -and a is in quadrant IV and sin(B) = and π/2 <B<T. Use sum and difference formulas to…

A: Given sin(α) = - 8/9 and α is in quadrant IV and sin(β) = 5/8 and π/2&lt;β&lt;π Use sum and…

Q: Question Find the differential dy of the function y = -2 cos (6x). Provide your answer below: dy=dx…

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Q: Let I = ₁ √2 + x² dx. Using the comparison properties of the integral, we conclude that (a) 2√√2 ≤ 1…

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Q: -. y ln x − x ln y = 4, y'

A: Given query is the derivative of the expression.

Q: 5. Use spherical coordinates to evaluate [[[ (x² + y² + 2²) ² dv D where D is the solid hemisphere…

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Q: x²-3x - 7 2 (x² + x + 2)(2x - 1) dx

A: Simplifying the given integrand: x2-3x-7(x2+x+2)(2x-1)=x2-3x-72(x2+x+2)x-12

Q: Given: y = cosh cosh (ex²)

A: Formulas:ddx cos hx =sin hxddx ex =exddx xn = n xn-1

Q: Using integration by parts, which of the following options is true of Sx arcsec x dx? Ⓒ / x ² arc A…

A: To use integration by parts for ∫x sec-1(x) dx

Q: Write an equation of the form y = a sin bx or y= a cos bx to describe the graph below. Ty 0 1 nin 1…

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Q: 1. An undamped spring-mass system with mass m = 2 and a spring constant k = 8 is suddenly set in…

A: Solution in step 2

Q: Je-2x sin 2x dx

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Q: Hi! Is this statement true or false? And why?

A: A detailed solution is given below.

Q: Use any method to find the Area of domain bounded by curve parametrized by X = cos³t₁ Y = sin³t, 0≤…

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Q: lim- LIMIT VALUE: z²-16

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question..…

Q: Write an equation of the form y=a sin bx or y= a cos bx to describe the graph below. ਨੀਲੀ 27 π 70 21…

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Q: Given: X == In(x²y - 1) y Find dy/dx. dy dx x²y-1 y-1 (E) None of these 1 2xy dy y x²y-1 dx + dy dx…

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Q: Evaluate the iterated integral. 1₁1²₁1x². (x² - y²) dy dx

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Q: 2. (4x³-3)dx

A: Let's find.

Q: Evaluate the following: 1) S x² √1 + x dx

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Q: 7. ft³10t+-3 dt

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Q: m(x) be the slope of the tangent line to the curve y = 2x3-6x² + 3x at the point (x, y). Find the…

A: Slope of tangent line is dy/dx

Q: using least cost method

A: The total cost using least cost method is Rs 284

Q: Decide whether the integral is improper. 1,01 In(x5) dx

A: We are asked to find whether integral is proper or improper

Q: thout eliminating the parameter t, find a Cartesian equation for the line tangent the curve C,…

A: Given the query is to find the equation of the tangent.

Q: 10. Consider the region bounded by the graphs of y = tan-¹x, y = 0, and x = 1. Find the area of the…

A: Let's find.

Q: Determine if y=5 cos x and x=31²-5t+3 dx

A: Given,             y=5cosx , x=3t2-5t+3To find : Determine dydt

Q: 2. Let f be the function from {a, b, c, d, e} to {1,2,3,4} with f(a) = 3, f(b) = 1, f(c) = 2, f(d) =…

A: givenf(a)=3f(b)=1f(c)=2f(d)=4f(e)=2

Q: y = 3x-2\4 4x-5

A: WE use the properties of logarithm to find the derivative

Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

Q: Solve the differential equation below using series methods. y’’ — 4xy' — y = 0, y(0) = 4, y'(0) = 2…

A: Here, the given DE is: y''-4xy'-y=0    ...(1) with y(0)=4,y'(0)=2

Q: The function f is defined as follows. 2x if -2<x<0 f(x) = x³ if x20 (a) Find the domain of the…

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Q: The base of a three-dimensional figure is bound by the line y = √x + 2 on the interval [-1, 1].…

A: We have to find the volume of bounded region in the interval [-1,1].

Q: Determine whether the improper integral diverges or converges. 6° x²ex dx converges O diverges…

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Q: If f(x) = sinx and g(x) = cosx, then what is the relation between g'(x) and f""(x)?

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Q: c. y = 4e (3x²-x) C.

A: