Find the length of the curve. 8) The spiral = e20, 0 s 0 s Ti r

Q: 1) Find dy/dr by implicit differentiation. tan n'(xy"+y)= x

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Q: Q3 : prove that : cosh?x + sinh²x =coch2x

A: L.H.S.:=cos h2x +sin h2x=(cos hx)2 +(sin hx)2  =ex+e-x22+ex-e-x22=14(ex+e-x)2+(ex-e-x)2

Q: Find r'(t). r(t) = (tan-(7t))i+t cos(t)j – Vēk

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Q: 31) Find two sets af poler Coorelinates for tue pornt (0,-4) Jer OLQL2T Auywers's 37 テノ, (16,…

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Q: Find V. (V x F) if F(x, y, z) = 8 sin zi + 6 cos(2.x – 3y)j + 7zk. V.(V x F) =

A: Vector

Q: For ​f(x)=x+5 and ​g(x)=3x+1​, find the following functions.   a. (f◦g)(x)​; b. (g◦f)(x)​; c.…

A: Topic = Functions

Q: Find (a) the critical numbers of f (if any) (b) the open intervals on which the function is…

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Q: Find r'(t). r(t) = (tan (6t))i+t cos(t)j – Vik I| NOTE: Enter your answer in terms of i, j, and k.…

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Q: sketch the given region R and then find its area. R is the region bounded by lines y=x, y=-x, and…

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Q: Consider the function f(x) = 5 – 4x² , – 4 < x < 2. - The absolute maximum value is and this occurs…

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Q: A farmer finds that if she plants 90 trees per acre, each tree will yield 30 bushels of fruit. She…

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Q: 3. If f(x) = [ 8+f dt ,find f'(1). .

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Q: d. [r:(t) r2(t)] and r:(t) x r2(t)] first by differentiating d Calculate dt the product directly and…

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Q: -2- At the point shown on the function above, which of the following is true? O f' > 0, ƒ'' > 0 Of'…

A: If the second derivative is positive then the graph of the function is concave up.

Q: Find the area of the shaded region. y y = x2 + 1 ... y = x -1 2

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Q: Use the graph of the function f to decide whether the value of the given quantity exists. If it…

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Q: Determine the signs (positive, negative, or zero) of y = f(x) (shown in the graph) and f'æ) and…

A: Consider the graph

Q: Determine the area of the glven reglon. y = x + sin x 3- 2- Step 1 Note that for the given reglon, x…

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Q: F'e) × r"(t)|| Use the formula x(t) = to find k(t). r(t) = 8 cos(7t)i + 8 sin(7t)j + 3tk K(t)

A: r(t)=8 cos7t i +8 sin7t j +3t kr'(t)=-56 sin7t i +56 cos7t j +3…

Q: 12) find the indefinite inteyral Inv dv 6 v3 Answery a) -L (2invtl /Ac 12 v2 bり- りよemvtiリ+c (2 12v2…

A: The given integral is ln(v)/(6v3).

Q: Find the limit: 4z4 – 4y4 lim (1,9) → (3,3) 4yª z² - y?

A: lim(x, y)→(3, 3) 4x4-4y4x2-y2

Q: Find the Maclaurin series for the function. (Use the table of power series for elementary…

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Q: Find the area of the triangle. Round to the nearest tenth. A 61° 13 mi 7.2 mi C В 14.3 mi? 12.6 mi?…

A: Given query is to find the area of the triangle.

Q: Find the first derivative with respect to the domain variable for the following functions. 4. f(x) =…

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Q: partial fractions to frd use 2 |- x9 + x8 2 3

A: Using partial fraction solving the given integration.

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

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Q: v F= F=

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Q: Find the sum of the series. s 7(-1)"72n + 2n + 1(2n + 1)! 00 Σ n = 0

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Q: Use the binomial series to find the Maclaurin series for the function. 1 f(x) (1 + x)3 Σ 00 f(x) n =…

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Q: Describe the graph of the equation. r= -3 i+tj+(t2-1) k O Itis a parabola in the x = 3 plane, vertex…

A: This is a problem related to parametric equation plotter. Based on the x, y and z value in terms of…

Q: 3) Find an equation for the tangent line to the graph at the specified value of x. y=x²V5-x² ,x=1

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Q: Determine whether the following equation is separable. If so, solve the given initial value problem.…

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Q: (2, 4) y = 2x ng a vertical element of area, he area of the shased region is gven by the integral

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Q: Find the domain of r(t) and the value of r(to). NOTE: Round your cnswer to two decimal piaces when…

A: Solving

Q: Integrate the following problems. Show all your work. 9. S(10xt – 5x3 + 3x)dx

A: Please refer to the image below

Q: dy 5 if y = 2x² + 5 and dt dx Find at x 4. dt dx dt

A: Solving the problem by finding the value.

Q: Consider the following. h(x) = ex2 − 4   Find  h '(x)=   Solve  h '(x) = 0 for x. x=   Find  h(0)=…

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Q: 3. Find the binomial series for (1+x)

A: On demand Question third is answer

Q: Use the figure to evaluate the following function, given that h(x) = tan x. (Simplify your answer.…

A: This question can be solved using the concept of trigonometry.

Q: 2- A radio station conducts a poll about gun control. It invites listeners to call one phone number…

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Q: e equation (2 cose – 1)(3 + tane) = 0 over the interval [0, 27]. solving for trig functions,…

A: We will solve the equation.

Q: Evaluate the limit using L'Hospital's rule if necessary sin(4x) lim z→0 sin(6x)

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Q: Evaluate the definite Integral. Use a graphing utility to vertfy your result. dx Step 1 To evaluate…

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Q: Find the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: differential cgnatuin as A. Identify the given to the dependent variable, degce z the eguati degre 3…

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Q: Graph the problem and solve using vertical or horizontal rectangle. Show your solution. Find the…

A: A detailed solution is given below.

Q: y = xx, x=4, and y =0 Revolve the area of the shaded region about the line x = 4. Using circular…

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Q: ind 4 using implicit differentiation and evaluate the derivative at point (-1,2) 2.a°y + 5x?y³ = 2x

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Q: The radius of a circle is increasing at a rate of 5 centimeters per minute. Find the rate of change…

A: We can find the answer as below using the given data.

Q: -+14х+13 dx 3x х+4

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