h of fun

Q: Find the equation of the tangent and the normal to the curve y=5x4 at the point (1,5)

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Q: Find the absolute minimum and absolute maximum of f(x,y)=3−10x+13y on the closed triangular region w...

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Q: If 5k -1 k >- > 0, for all k >1 and E is a divergent harmonic series then - k = 1 k

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Q: If f is continuous and ∫31 f (x) dx = 8 , show that f takes on the value 4 at least once on the inte...

A: Given that f is continuous and ∫31 f (x) dx = 8. We have to prove that, f takes on the value 4 at le...

Q: The arc length of the curve r= cos 30 with 0<0 ST is попе V(sin 30)² + (cos 30)² d0 0. T V-9(sin 30)...

A: We have to find

Q: (D) Sketch the graph r= 1- cos 0 and find the area enclosed by r=1- cos 0.

A: Solve by double integration

Q: Let R be the region bounded by x=y2, x 0 and y= 2, then the volume of the solid formed by revolving ...

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Q: Let R be the region bounded by the graphs of y= /x, x=9 and the x- axis, then the volume of the soli...

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Q: | sin? 8x dx = попe

A: We have to find the integral.

Q: Find the gradient ∇f of the function f given the differential. df=2ye^xdx+xe^xdy   ∇f=

A: Note that            . Here, df=2yexdx+xexdy. So, here we have fx(x, y) = 2yex and fy(x, y) = xex.

Q: DO NOT USE METHOD OF SUBSTITUTION AND SIMPLYFY YOUR FINAL ANSWER

A: As we cannot use substitution we need to expend the given function as

Q: 14

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Q: Let R be the region bounded by y=x+3, x= -3 and y= 3, then the volume of the solid formed by revolvi...

A: Volume of solid revolving by axis problem..... 

Q: The improper integral 1 dx converges to '5 Vx-5

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Q: Please help me with this question. Much appreciated

A: To find the value of f(t+1) we just replace t by t+1 in the given function and then by taking the ra...

Q: Evaluate tan (7x+1) sec³(7x+1) dx .

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Q: if a 2 51 4 2 -5 -4 -3.-2 -1 2 3 4 5 -1 -3 -4 -5+ Clear All Draw: 1. 2.

A: We can use the graphical analysis in order to solve the given problem.

Q: Which of the following is not an improper integral? 1 dx cos x 0. cos x dx cos x dx 1 dx cos x

A: We have to check 

Q: Find the length of the portion of the arc given by r(t) = (e 'cos t) i + (e 'sin t) j + 5e ' k, -In ...

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Q: The sequence a, is converges to 0 a divergent sequence попе converges to 8

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Q: The arc length of the curve r= cos 30 with 0<0 <T is T V(3sin 30)² + (cos 30)² d0 0. попе V-9(sin 30...

A: Length of curve problem.... 

Q: use long division or completing the square and substitutions to evaluate

A: Since multiple questions are asked. I am answering the first question. Please repost for other .

Q: Find the absolute minimum and absolute maximum of f(x, y) = 13 – 8x + 10y on the closed triangular r...

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Q: Part 3 The diagram on the sides show the flange that is used to mount the hollow shaft. Propose suit...

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Q: Example 4 A man launches his boat from point A on a bank of a straight river, 3 km wide, and wants t...

A: Given:  Example 4 A man launches his boat from point A on a bank of a straight river, 3 km wide, and...

Q: please show the answer step by step

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Q: 5

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Q: A bungee jumper leaps from a bridge. Velocity is determined by the given differential equation. dv C...

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Q: The arc length of the curve r= cos 30 with 0<0<nis попе J V-9(sin 30)² + (cos 30)² d0 I (sin 30)² + ...

A: In this question we have to find the arc length of the curve.

Q: Recall that there are 2π2π radians in one full rotation and 360 degrees in one full rotation. Supp...

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Q: general equation of the differential equation find the solution

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Q: The sum of integrals below give the area of a region in the xy-plane. Sketch the region, label each ...

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Q: Which one of the following polar equations is equivalent to y =x-4. 4 sin 0 - cos 0 4 cos 0+sin 0 co...

A: We have to find which of the following polar equation is equivalent to y=x-4.

Q: Draw the region of integration.

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Q: By using integration by parts, the value of the integral In 2x dx is попе o x In 2r -x + x In 2r - x...

A: Option C is correct

Q: Find the value(s) of c guaranteed by the Mean Value Theorem for Integrals for the function over the ...

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Q: (C) Expand f(x) = tan-! x in a Taylor series about x = 0 and use this Taylor series with n=3 to appr...

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Q: ٣

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Q: dx = - sin 20 and de dy = cos 20. de Given that r= cos 0 ; The slope of the tangent line to the pola...

A: Use the formula for the slope of a polar curve.

Q: From 0 - infinity

A: Given  ∫0∞e-2xdx

Q: One polar coordinate representation for the rectangular point (2, – 2) is (2/2.* (2/3. - :) -(2/3. -...

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Q: 3 The arc length of the portion of the curve y=x2 with 0<x<4 is Osz9.0734 OSx 10.1938 s=7.7868 попe

A: We have to find the arc length of the portion of the curve y=x32 with 0≤x≤4. 

Q: Google's Revenue The revenue for a certain corporation from 2004 (t = 0) through 2008 (t = 4) is app...

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Q: Expand f(x) = tan x in a Taylor series about x= 0 and use this Taylor series with n = 3 to approxima...

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Q: 1. Show that 2465 is a Carmichael number.

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Q: (4. ) The rectangular coordinates for the polar points [4, is

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Q: QUESTION 7 Which of the following is not an improper integral? TC 2 cos x dx 0. 1 dx 0. cos x dx 1 d...

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Q: (A) Sketch the region R bounded by the graphs of y = 6-x², y =x and y=6. Find the volume of the soli...

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Q: n+1 The sequence is n = 1 decreasing for all n21 increasing for all n>1 increasing for all n>2 попе ...

A: We will solve the following. 

Q: Find the area enclosed by one leaf of the rose r= 12 cos (50). The area is (Type an exact answer, us...

A: We need to find the area enclosed by one leaf of the rose r=12 cos 5θ. Let us first plot the figure....

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: