Answer the following True or False: Let f(x) be a differentiable function, such that f(– 1) = - 5 and f(3) = with – 1 < c < 3 such that the tangent line to y - 5. Then there exists a c f(x) is horizontal at x = c. O True O False

Q: Describe the graph of the equation. r = 7 cos t i - 16 sin i j+k O An ellipse in the planex = 1,…

A: We have to describe the graph of the equation.

Q: 9) use the snell metnod to sef up end eveluete tueinteyrel tret gives the volume of the solid…

A: Using shell method, volume is evaluated.

Q: cant see image of solution

A: Please refresh the page if you do not see the math expressions clearly.  Here is the image form of…

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A:

Q: dy for x'e*y Find dx sin' ( 3x) + In (y) by using implicit differentiation.

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: X+3 Q4) Find the integration by using: dx J 2x3-8X

A:

Q: Evaluate the area of the region bounded by y2 = x and y2 = 6−x.

A: To find : Area between y2=x and y2=6-x First let's find the intersection points x=6-x⇒x=3 Therefore,…

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A: Write the nth term and  add them to get Sn .

Q: roduct directly and then by applying the formulas dr dr r(t) and dt dr, dr x ). dt Fi(t) - cos(t)i +…

A: To differentiate.

Q: View Policies Current Attempt in Progress Find r'(t). r(t) = (tan-(9t))i+t cos(t)j – Vik | NOTE:…

A:

Q: 10 10 If f (x) dx=17 and f (x) dx=12, then f (x) dx=5 . 8. (A) True (B) False

A: To determine whether the given statement is true or false.

Q: Find the curvature and the radius of curvature at the point t = 0. e' cos(t), y = e' sin(t), = 3e* x…

A:

Q: satisfies thé équation:y + 13y - Show that y=e Sin 3x

A: Topic = Derivative

Q: 2. S x²-6x-4 xp x+2

A: Given: I=∫x3-6x-4x+2dx As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫a·fxdx=a·∫fxdx

Q: Find curl (7z i + 8xj+2y k). curi (7z i+ &x j+ 2y k) = (1 i+( j +( )k

A:

Q: ; Test the following series whether it is convergent or divergent (show all your works) n2 +7 a) 2…

A:

Q: anUNIVE Q3) Find the integration: - (x+1)vx2+2x

A: As you have asked multiple questions so I have answered only first question as per the…

Q: Example 22 Find the eccentricity and directrices of the hyperbola given x? y? 1 9 16 Sketch the…

A: Given: x29-y216=1

Q: Determine if the following series converge: 2.4.6 . · (2n) ... (a) (b) ) Inn 3.6 - 9 · · · (3n) ...…

A:

Q: Find the area of the region shared by the cardioids r= 12(1 + cos 0) and r= 12(1 – cos 0). The area…

A: Given: r=12(1-cosθ) r=121+cosθ

Q: Evaluate the definite integral. ell! i + e¯'j + t k )dt O ell – 1 (e-1 – 1) - (ell – 1) i – (e-1 –…

A: The given integral is: I=∫01e11ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: 8) Fiad the volume of the solid gonereted by revelving the regien beunded by tue graphs of equetians…

A: Given problem:- Find the volume of the solid generated by revolving the region bounded by the graphs…

Q: Solve the equation on the interval 0s0<2n. cos (30) = - 1 Vhat are the solutions to cos (30) = - 1…

A: We have to find the angle

Q: Evaluate sin? xcos xdx .

A: To evaluate: ∫sin2x cos3x dx=∫sin2x cos2x cos x dx=∫sin2x (1-sin2x) cos x dx

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A: We are given a ferris wheel with the following informational : diameter : 64 m No of cabins : 32…

Q: Solve the following problems. 1. (x²-2y²) dx+3xydy=0

A: This question can be solved using the concept of homogeneous differential equation.

Q: Represent the plane curve by a vector-valued function. x2 + y2 = 16 r(t)

A: The given plane curve is   x2+y2 =16.  We have to represent the curve by a vector valued function…

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A: we have to find the area.

Q: Find r'(t). r(t) = (tan '(7t))i+t cos(t)j – /tk NOTE: Enter your answer in terms of i, j, and k.…

A:

Q: -24 e 5n costx dy Ln(sinx) dx

A: To solve the following problem

Q: 1. Calculate the following limits (showing all working): log,(n) + 5" n-0o log7(n) + 7" Vn5 + 2 +…

A:

Q: Evaluate the definite integral. 1+eJ+/k]di i-ej+ k o ? - 1 1 + (-" – 1) j + k e-1)1- (e - 1) J+ k o…

A: Given: I=∫01e9ti+e-tj+tkdt As we know that; The Power rule: ∫xndx=xn+1n+1+C And ∫eax+bdx=1aeax+b+C

Q: Integration

A: We will solve the integral.

Q: Evaluate the definite integral. ellt i+ej+t k)dt O ell – 1 (e – 1) + (ell – 1) i – (e-l – 1) j + k…

A:

Q: Find the gradient vector field Vf of f. f(x, y, z) = xSye'/z Vf(x, у, 2) %3D

A:

Q: Q2) Find the integral of: f*,6 tan*x dx

A:

Q: Evaluate the defınite integral. 8 i + e¯´j+tk)dt 0, – (e-1 – 1) j+ k i-e'j+;k 8 (e* – 1) i – (e- –…

A: The given integral is: I=∫01e8ti+e-tj+tkdt   We know that; The Sum rule: ∫fx±gxdx=∫fxdx±∫gxdx The…

Q: e cosx sin x dx 1-e2 cosx

A: Given problem:-

Q: Let y=f(x) be a solution of the first order linear differential equation y'=y-10x² such that f(0)…

A:

Q: Consider the following. 3x - y + z = 6 Sketch a graph of the plane.. y -6 y -4 2 y 4. 2 2. Label any…

A: Given :3x-y+z=6To find it's intercept

Q: - sin² ydy 6. 4 tan" y

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

Q: Q5) Find the integration by using (by part method): S e3X sin X dX

A:

Q: Use the formula r(t) = |r(t) × r"(t)|l| ||r(t)||³ to find k(t). %3D r(t) = t’i + t3j K(t)

A: r(t)=t^2i+t^(13)j r'(t)=d(t^2i+t^(13)j)dt=2ti+13t^12j r''(t)=d(r'(t))dt=2(1)i+13×(12t^11)j…

Q: SUTM i) Find the domain 1. Given z = f(x, y) = /36 – 9x² – y-. of the function. ii) 3 UTMd rano UTM…

A: Let's find.

Q: If z = 52? – 3y? + 4y, find the differential dz. You should have variables dz, dy, y, and z in your…

A:

Q: by which criteria?

A: Apologies for the inconvenience. Here is the correct solution.   If a series ∑n=1∞an has either…

Q: Show that g : B → A, g(x) = √ln x is the inverse of f. Why is f^−1(x) 6 ≠ −√ln x?

A:

Q: 4. Consider the matrix А 5 2 One of the eigenvectors of A is given by [1 -1]'. Find the eigenvalues…

A:

Q: e i+ - 1 (P-1)i-(e1-1)j+글 i - k

A: Given query is to find the integral.

Q: y = Vx + 3 from x=1 to x=4

A: We find the area under given curve and bounded by axis and given lines x=1 &amp; x=4 using definite…