Show that for every point on the curve r(t) = ⟨etcost, etsint, et⟩, the angle between the unit tangent vector T(t) and the z-axis is the same.

Q: Find the limit lim 14,cos(, 18z Note: Give the exact answer but not the decimal approximation (for e...

A: Given:   limx→0+x14 ecosπ18x

Q: operty. -7(4y - 9) - 7(4y - 9) = (Simplify your answer.)

A: SOLUTION-

Q: The function e* (x² – 1) is equivalent to the series: Select the correct response: 19 - x³ + -x' + 1...

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Q: 3sin4t di 5(1– 3cos21)

A: To solve the integration. 

Q: Find the equation of the line tangent to the graph of f(x)= (In x)2 at x= 3. y%3D (Type your answer ...

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Q: -sin20 + C , then f (0) =-cos20. 2 A True B) False

A: Solution: f(θ)=12cos2θ

Q: 1. Find the limit of the following: x° – 11x +37x* +6x' – 297x? +621x – 405 lim. x* —11x* +47х* -114...

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Q: 7/4 26. * sec*e tan 0 de sec*0 tan*o de

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Q: Let f (x, y) = 3y O 1 x/3 1/(3у) (1/3)y

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Q: 10 – 2x6 dx

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Q: Find the derivative of the vector function r(t)=ln⁡(7−t^2)i+sqrt(8+t)j−5e^(2t)k r′(t)=⟨  ,  ,  ⟩

A: The given vector function is r(t)=ln(7-t^2)i+8+tj-5e2tk We have to find the derivative of the vector...

Q: The cost of certain piece of machinery is $ 700 and its value is depreciating with time according to...

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Q: Prove that the line x +1 = 글(-6) - lies in the plane 3x + y – 2 = 3.

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Q: 2. Evaluate the following functions using the given relations. f(2) = -1 ; Relation: f(n+1) = 5 - [f...

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Q: 21 - v oX

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Q: A glacier in Republica was observed to advance (h)2.5______ inches in a (i)____71_______ minute peri...

A: This is a basic problem of calculus

Q: Find the limit, if it exists: (Do not use L'Hospital's rule) 94x2 + 19x + 5 lim x→00 182x25 + 3x – 9...

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Q: 3. (а) х-ахis (b) y-axis y-4-

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Q: Compute the following limits. 4-(2+h) (a) lim (b) lim - x-2 h→0

A: Using rules of limits.

Q: 2-28 Determine whether the series is absolutely convergent. conditionally convergent, or divergent. ...

A: NOTE: Refresh your page if you can't see any equations. . the given sequence is  here the sequence...

Q: Question 23 Give the coordinates of the center of the circle with the equation x²– 6x + y²=12-4y. Bl...

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Q: Find the domain of the vector function r(t)=⟨ln⁡(19t),sqrt(t+8),1/sqrt(7−t)⟩ using interval notatio...

A: Given vector function isrt=ln19t,t+8,17-tfind the domain.

Q: 2 . Complete the following tables of values to investigate (x - 2x + 4) f(æ) f(x) 0.5 1.6 0.7 1.35 0...

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Q: The curve C is the portion of the graph of y = 16* for 0 <z < 2 (distances measured in m). The curve...

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Q: Find the exact length of the curve. 36y? = (x2 – 4)3, 4 0 23.335

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Q: and horizontal lines), without performing the integration. (c) Write down the integrals with their l...

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Q: Consider the following. f(x) = x* + 3 Find f'(x). f'(x) = Find the value of dy when x = -4 and dx = ...

A: f(x)= x4+3  Find 1) dy/dx  2) dy when x= -4 and dx= -0.01  3) ∆y when x= -4 and ∆x=-0.01 

Q: Find a parametrization of the ellipse centered at the origin in the xy-plane that has major diameter...

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Q: Find the derivative of f (x) = (4x + 1)(5x² + x/x ). Upload your work in the next question. The deri...

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Q: 2e*dx where e = 2.7183 %3D

A: Given: I=∫012exdx   As we know from the integral; ∫a·fxdx=a·∫fxdx, where 'a' is the constant. And ∫e...

Q: Find the derivative of a function f(x)=(x^2+1)^3 (2x−1)^4 f ' (1) = ____

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Q: dP 16. dt 11-18 Find the solution of the differential equation that satisfies |Pt, P(1) = 2 7.3: 16 ...

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Q: Variable Separable (8) dx dy e 3x+2y; Provide the explicit solution (9) secx dy = sec 2ydx

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Q: 3. Calculate the area of the region R enclosed within the following boundaries: (x² + (y – 1)² < 1 y...

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Q: Find the limit , if it exists:(Do not use L'Hospital's rule) 16 lim 2→16 16 Note: Give the exact ans...

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Q: 14. Consider the function f(x) = xª – 2x?. %3D - a) Find the interval(s) where the function is incre...

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Q: Question 7 04 d0 =+C 2 A True (B) False

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Q: Find an equation of the line tangent to the graph of G(x) = 7 e -5x at the point (0,7). The equation...

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Q: the given expression :3y^2 + 6y + 7 is equal to. SUBMIT YOUR SOLUTION * none of the choices O 3(y + ...

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Q: Set up, but do not evaluate, an integral for the length of the curve. y = x - 3 In(x), 1< x < 4 4 dx

A: The given curve y=x-3 ln(x), 1≤x≤4

Q: Let g (x) = 12/x+ 10x . Use the limit definition of derivative to find the derivative of g (x) at 2....

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Q: Question Evaluate the following limit using L'Hospital's rule. 1 lim 4x cos 6x4 Provide an exact ans...

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Q: DEvaluate the Riemann sum for f(x) = x- 1, -6<x<4, with five subintervals, taking the sample points ...

A: A function is given that is f(x) = x - 1. We have to find the Riemann sums for f(x) on the interval ...

Q: Write an equation of the tangent line to the curve f (x) = 10//7 + 6x at the point (4, ƒ (4)). Uploa...

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Q: Find the area under the graph of the function f(x)= 7sin(x) bounded by the x-axis and the lines x=0 ...

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Q: Find the point(s) on the parabola x =y closest to the point (0,3)

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Q: 3- -3 -2 -1 1 2 3 Refer to the graph below to answer the following 5 questions. Record your answer t...

A: Part (a) As we see when x tends to -3, the left hand limit and the right hand limit of the function ...

Q: Find the following limit, then enter your answer in the form a/(x+b)(x+c) 1 If f (x) = find lim x+2 ...

A: This question can be solved using the concept of limit and function

Q: Let T3 be the Maclaurin polynomial of f(x) = e*. Use the Error Bound to find the maximum possible va...

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Q: Determine the solution to the initial value differential equation y' = 0.0012 y (2900 - y) y(0) = 13...

A: We have to find equation , Y max and x value for 90% Ymax