an = 2n + 5 245) 4n+1

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: The given polar curve .The aim is to find the slope of the tangent line to the polar curve at the…

Q: Evaluate the following integral using trigonometric substitution. x² √√64-x² S dx

A: I=∫x264−x2dx

Q: Find the form of (but do not solve for any coefficients in) the appropriate particular solution Y…

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Q: Math 152 metric IHU 3. In this problem we'll evaluate the integral cos²(z) sin³ (2) dr. (a) First,…

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Q: Step 3 Write the two binomial factors so that the first term of each factor is x and the second…

A: To write the complete factorization of

Q: The radius r of a circle is increasing at a rate of 3 inches per minute. Find the rate of change of…

A: Please solve the given problem using the concept of derivatives.

Q: Suppose f(x, y) = (x - y) (25 - xy). Answer the following. Each answer should be a list of points…

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Q: Evaluate the integral. +C 2x + 9 x² + 6x +34 17 -da

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Q: Find f. f(t) f'(t) = t³ + -/-/7₁ t5 t> 0, f(1) = 4

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Q: Find the critical numbers and the open intervals on which the function is increasing or decreasing.…

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Q: 1. If y2 = 10x, then A. - 5 2xy 1 C. -2232 2x d² y dx2 = B. D. - 1 5x 2y 5xy 2

A: Given,

Q: Evaluate the following integral, f (x - 5y) dx - 8y² dy where C' is given by x = y² + 6 from (7, 1)…

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Q: Sketch the region enclosed by the given curves. Decide whether to integrate with respect to x or y.…

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Q: List the first five terms of the sequence. a1 = 2, : 2, a n + 1 an + 1 = 2an + 4 21 2 а2 8 12 14 16…

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Q: Find dy/dx by implicit differentiation sin y = x^3 + y^4

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Q: Consider the equation below. f(x) = 4x³ + 9x² - 54x + 1 (a) Find the intervals on which f is…

A: In this question, we will find the interval of increasing and decreasing.

Q: Z₁ cos# = 2 V₁ 1 V +(x-2- sin e Z₁ cos Z₁ X + V₂ V₂ cos 9) +1/+ Z₁ 1 V. cose V 2 -sin 0 +

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Q: Help determine the difference quotient and for f(x)=x^2+4

A: Given,. Difference quotient=

Q: Let f(x) = 5 − 3x²2 and g(x) = x + 5. Compute the following. (a) (fog)(x) (b) (c) (e) (fog)(-1)…

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Q: 1 V₁ V2 = 2(+/-+- (1 (v₁/v₂) = 2 sin = -2V²-V²_2₁ Z₁ cos 1 =2²₁√√√√²₁ X Z₁ + V/₂ √/1-(V₁/V₂)² V₂ V2…

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Q: For which value of t does the line given by the parametric equations x=t-1, y = 1+ 2t, z = 3-t pass…

A: x=t-1y=1+2tz=3-tPoint (-2,-1,4)

Q: Show that the function is increasing on the given open interval. (Enter your answers as a…

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Q: Second Derivative Test 1. Find the first derivative of the function g(x) = 6x³ +54x² + 144x. g'(x)…

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Q: (a) Find and sketch the domain of the function f(x,y)=√x-1+√y-4

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Q: To test this series for convergence ∞ n=1 n n6 + 7 You could use the Limit Comparison Test,…

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Q: Calculate the L4 approximation for f(x) = cos² x on TU I 4 2

A: The left Riemann sum∫abf(x)dx≈Δx(f(x0)+f(x1)+f(x2)+⋯+f(xn−2)+f(xn−1))Δx=b−an

Q: Find a formula for the general term an of the sequence, assuming that the pattern of the first few…

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Q: Show that the functions are linearly dependent on the real number line: y1 = 17; y2 = 3cos2x; y3 =…

A: The given functions are  and .The objective is to show that the functions are linearly dependent on…

Q: Solve the following non-homogeneous differential equations: 1) x"(t) + x(t) = 2 cost

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Q: Profit The profit P (in dollars) made by a cinema from selling & Bags of popc x² 28,000 3,300, 0≤x≤…

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Q: Let (a) (b) (√x + ²) dr + (y² + ln(2x)) dy=0, x>0. Check that this is an exact differential…

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Q: Find the surface area of the part of the plane 2x+5y+z=4 that lies inside the cylinder x^2+y^2=1.…

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Q: Given the following integral and value of n, approximate the following integral using the methods…

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Q: Consider the function f(x) = 2x³ – 2x on the interval [-5, 5]. (a) The slope of the secant line…

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Q: Evaluate the following limit. lim x→0 3 (²2 x 3 sin(2))

A: L=limx→0(3x−3sin⁡(x))

Q: 3 11 (1 + ³²) ² lim (1+

A: L=limx→∞(1+3x)x11

Q: 2. Isolatex. For answer, show this structure <x< -5 ≤ 2-x < 5

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Q: Use the quadratic formula to solve the equation. Give two forms for each solution: an expression…

A: The given quadratic equation is

Q: At what point(s) on the curve x = 6t² + 9, y = t³ - 5 does the tangent line have slope 2 (x, y) =

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Q: Find fx fy and f, and evaluate each at the given point. f(x, y, z) = xy x+y+z (3, 1,-1) fx(x, y, z)…

A: The given function is

Q: Given that (fog)(x)=x-8, which are correct rules for f(x) and g(x) that result in this composite…

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Q: ii) Read the graph below and say whether limx→-3 f(x) exists: y=h(x) -9-8-7-6-5-4-3-2 9876 8+ 7+…

A: This is question of calculusHere graph is given We have to find limit of function.Further…

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y (a) 128 (b)…

A: Note: As per our guidelines, we can solve first three sub parts as your all parts are not small.

Q: (2) Solve the given homogeneous equation by the appropriate substitution y dx (x + y) dy = 0. - You…

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Q: Solve the given initial-value problem. Y(x) = y" + 4y' + 5y = 35e-4x, y(0) = -5, y'(0) = 1

A: y'(0)=1

Q: 6. Logarithmic differentiation Use logarithmic differentiation to evaluate f'(x). f(x)=(1+x²)in x

A: The given function .The aim is to find the derivative of the function using the logarthim…

Q: A student solves an optimization problem as in Model 1, except that in the problem Mini and Max are…

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Q: Verify that f(x) = 2x^3 + x^2 − x − 1 satisifies the hypotheses of the Mean Value Theorem on the…

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Q: Labor. Refer to Table 4. (A) Find the average rate of change of weekly hours from 1980 to 1990.…

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Q: Find the area of the surface given by z = f(x, y) that lies above the region R. f(x, y) = 4 + x² -…

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