A. Find the derivative of the function: f(x) = x4Ln (5x) B. Find the intervals where f(x) is increasing

Q: ·/₁ Evaluate cos x sin³ x dx. 2 cos(x) + cos¹ (x) ²/ X syntax error. + C

A: Given query is to find the integral.

Q: y' = y = sec(0) tan(0) sec (0)tan (0)sec² (0) X

A: Given query is to find the derivative.

Q: Find the exact value of the expression tan sin -¹|- √√3 2 tan sin -(-/-))-0 2 (Type an exact answer,…

A: Topic = Trigonometry

Q: Evaluate the limit: lim x-6 x² 2 13x + 42 x - 6

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Q: a) b) Let V R³. Let W be a subset of V where W = The vectors = Show that W is a subspace of V. a…

A: Please see the below picture for detailed solution.

Q: -52 The region R in the first quadrant is bounded by the coordinate axes, the curve y = e x = 1. The…

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Q: 5. What is the change in surface area with respect to time at t = 4s? Given that 12t^5 cm^3/s

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Q: If f(-3) = -6, f'(-3) = -5, f(-1) = -18 and f'(-1) = -12 then: [ x . f"(x) dx

A: Given:- f-3=-6,f'-3=-5,f-1=-18,f'-1=-12

Q: E A 4 B D G C

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Q: s dx = S-₁₂ ² =S= X 2 – ν -1-3v+v² dv

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Q: Find the solution to the Bernoulli equation. xdy = ( + 7 - x) dx ○ y³ = 1+ Cx-³ Oy³ = 1+ Cx³ ○…

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Q: 2) Evaluate using long division first to write f (x) as the sum of a polynomial and a proper…

A: According to question,Given Integral,∫x3+ 1x2 + 1 dx

Q: Variable Separable (Solution Step) The variables of the equation M(x,y)dx + N(x,y)dy=0 are…

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Q: [8] b) Find the equation of the plane in R³ that contain r(t) = (-3t, 1+ 4t, 6-2t).

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Q: If z = sin(x/y) and x=ln(u) and y=v^3 , find the following partial derivatives using the chain…

A: z=sin(xy)x=lnuy=v3∂ ∂x(sinx)=cosx∂ ∂x(xn)=nxn-1

Q: Using Maclaurin's theorem to show that 0 < 1/108. (ex=1)< <1

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Q: 8. Find the equation of the tangent line and the normal line at the point corresponding to the given…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: For what value of k will the function f be continuous on (-∞, ∞)? f(x) = = +2 9 x + 3 k if x # -3 if…

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Q: Activity 3.6 Discuss the continuity and sketch the graph. 3. f(x)=√xatx=8 1. f(x) = 3x² + 2x + 1, x…

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Q: Suppose a company has fixed costs of $300 and variable cost per unit of x +1460 dollars, where x is…

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Q: If E is the solid described below with density function p(x, y, z) = x² + y2, find the following…

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Q: ) a. Put the equation into the standard form b. multiply both sides of the equation by the…

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Q: a. f(x) = 15x²-3x-5 + c. f(x) = a. 1 x2 x³ + 2x² - 9x +5 X 4. Write the equation of the tangent line…

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Q: Leave all answers in exact form (not rounded) Evaluate the improper integral or state that it is…

A: Given integral:- ∫1∞1xx2+2dx

Q: Find a non-trivial linear combination of a, b and c whose sum is the zero vector. 0 a+ b+

A: Given from the graph, a=&lt;-8,-2&gt;,   b=&lt;5,-8&gt;,   c=&lt;-5,-6&gt;

Q: The graph below is the function f(x) -5-4 -3 -2 -1 4 on 3 da T -4 Find f(2) Find lim f(x) x 2 Find…

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Q: If an arrow is shot upward on Mars with a speed of 64 m/s, its height in meters t seconds later is…

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Q: & 5. Radioactive decay. Gold-198 has a decay rate of 25.72% per day. The rate of change of an amount…

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Q: Find the unit tangent vector to the curve defined by r(t) = (5t, −2t, √25 – †²) at t = -2. - T(-2) =

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Q: Write the Taylor series for f(x) = sin(x) at x = Find the first five coefficients. Co= C1 = C₂= C3=…

A: Given function:- fx=sinx

Q: 1. Consider the following, recursively defined function C(1) = 1 C (2) = 1 - C(n) = C(C(n − 1) + C(n…

A: We need to prove that C(n)=1 for all n.

Q: 3. (x + y - 6)dx + (x − y + 4)dy = 0.

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Q: Hello can you type it and shouldnt it be -265 if we put it where the zero is

A: We need to find the equation of the plane passing through the points 7,7,5, 1,3,6 and 5,-2,-1.

Q: Find for In (7y) = e sin (2x). dy dx dy =

A: ln7y=eysin(2x)d dx(lnx)=1xd dx(sinx)=cosxd dx(ex)=exd dx(a.b)=adbdx+bdadx

Q: The derivatives of the function f(x) = cos(3x²) that follow are incorrect. What misconception occurs…

A: Question number 6th  is not properly visible so we will be answering only 8th question.

Q: Find the directional derivative of f(x,y)=x2y3 + 2x4y at the point (-1, 3) in the direction Θ=pi/4.

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Q: Evaluate the following limits, if they exist. Where applicable, show all work. lim lim x²-3 lim…

A: As per our guidelines we are restricted to solve maximum 3 subparts of a problem.  Further please…

Q: Find the area of the region enclosed between f(x) = x² − 3x + 3 and g(x) = 2x² – 3x – 1. Area =…

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Q: Determine whether the following curve uses arc length as a parameter. If not, find a description…

A: Concept: By substituting bwith tand using an other variable besides t, such as u, we can convert the…

Q: Graph the line containing the point P and having slope m. P=(-2,-5); m = - OA Q 53 OB. -10 > S O C.…

A: we need to find the graph which has slope=-1/2 and has the point (-2, -5)

Q: Please answer #9

A: The region would be between the curvesy=x and y=x. Intersection: x =x,x=0,1 The region can be…

Q: xy² (x,y) →(0,0) x³ + y³ b) Show that lim does not exist.

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Q: Let f(x) = 2x√x + f'(x) = x³√x

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Q: Given the function P(x)= x³5x² - 24x, find its y-intercept is its x-intercepts are 1 X1 < x2 < 3…

A: Given function:- Px=x3-5x2-24x

Q: eliminate the arbitrary constant y=C1x^2+C2e^2x

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Q: y= 11 In x 3+ Inx

A: Given query is to find the derivative.

Q: Use the intermediate value theorem to find the value of c such that f(c) = M. f(x) = x² - x + 1 on…

A: This is question of calculus  here value of function we have to find. further calculation is given…

Q: aw aw raw a dependency diagram, and write a chain rule formula for and , where w= g(q) and q = f(m,n…

A: This is a problem of partial differential equation. Please follow the procedure given below.

Q: Find an implicit solution to the differential equation e³ dx + (2y + xe") dy = 0.

A: We have to find an implicit solution of the given differential equation.

Q: Compute the surface area of revolution about the x-axis over the interval [0, л] for y = 8 sin(x).…

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