Find an equation of the tangent line to the graph at the given point. (y - 3)² = 4(x - 5), (6, 1) y X Parabola 2 Ç (6, 1) 6 10 12

Q: Find the direction cosines and angles of u and show that cos²a + cos² ß + cos² y = 1. (Round your…

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Q: Consider the following differential equation to be solved by the method of unde y" + 2y = -18x²e2x…

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Q: Baseball A (square) baseball diamond has sides that are 90 feet long (see figure). A player running…

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Q: Sketch the curve represented by the parametric equations (indicate the orientation of the curve),…

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Q: 7. Σ n=2W 3 2 n2 + I 00 8. Σ n?e=n n=1

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Q: Evaluate the following integral 6x + SS (8x - y) In (8x - y) dA R where R is the region bounded by…

A: Given that, where R is the region bounded by the graphs of                  Using the change of…

Q: 2. Find the derivative: a. y=ln(e^x)/(1+e^x)

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find the surface area of the surface given by the portion of the paraboloid z=x^2+y^2  that lies…

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Q: X 3. Verify that f(x)=- satisfies the conditions of the Mean Value Theorem on the closed interval…

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Q: Evaluate the following integral. A sketch is helpful. R 3 15x² dA; where R is bounded by y = 0, y =…

A: To find:- Where R is bounded by

Q: Suppose a triangle in space has vertices (a, b₁, ²₁), (a₂, bz, C₂) and (93, b3; (3). Explain how you…

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Q: HOMOGENEOUS DIFFERENTIAL EQUATION Solve the following differential equations using HOMOGENEOUS DE.…

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Q: Find the absolute maximum and absolute minimum values of f on the given interval. 4 f(x) = x +-…

A: Critical point of the function is the value of the function at which derivative of the function is…

Q: 2 xy dy + 4y dx = 8 x dx 2 2

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Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) =x² + y² subject to the…

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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: 2.21 A mathematical model describing the state of a learner y(t) at time t while learning a specific…

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Q: Evaluate the derivative of the following function. f(x) = 2x sinh − 1x − 2/x+1 f'(x)= 2 arcsinh(x)

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. If the…

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Q: Evaluate the integral. Answer= +C -22e-30 e2x + 6e +5 12276 -da

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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: Find f. f(x) = f"(x) = 8x³ + 5, f(1) = 6, f'(1) = 2

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Q: Describe the x-values at which the function is differentiable. x² y = x² - 49

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Q: dy d²y Find and dx dx² x = t² + 2, y = t² + 3t dy dx d²y dx² For which values of t is the curve…

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Q: The radius of a right circular cone is increasing at a rate of 1.2 in/s while its height is…

A: given

Q: 1 Let f(0)= sin(0) + cos(0). √√3 Calculate the derivative. [Note: to get the to show up type theta,…

A: Consider the function

Q: A point is moving along the graph of the given function at the rate dx/dt. Find dy/dt for the given…

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Q: Consider the following. Find y'(x). y'(x) = y = X = X x² +9 Find the critical numbers of y(x).…

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Q: 4. Use Calculus to graph g(x)=x² + 4x³. Make sure that your graph shows all intercepts, extrema, and…

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Q: (a) The graph below is the derivative of f(x), but you are answering questions about the parent…

A: Note: As per our guidelines we are supposed to answer only first 3 subparts.If there are multiple…

Q: If f(x) = f'(x) = ƒ'(1) = = 2 sin x 3 + cos x > 3 cos (1) () then 3 cos (x) + sin(x) (3 + cos x)² X…

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

A: The equation of the curve is given byTo determine: The slope of the tangent line to the given curve…

Q: Suppose that P(t) (with t in months), the fish population in a lake contaminated by chemicals,…

A: Given Differential equation as follows

Q: 1) State the order of the given ordinary differential equation. Determine whether the equation is…

A: To determine the given equation is linear or non linear.

Q: Question 6 Calculate the resultant of the forces shown in the concurrent force system. 6N 40% 30N…

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Q: Suppose f(x, y) = x² + y² - 8x and D is the closed triangular region with vertices (8,0), (0,8), and…

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Q: Sketch the graph of f by hand and use your sketch to find the absolute and local maximum and minimum…

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Q: 17 [²²; 1 The integral dx diverges. x (In x )1.5 If the integral converges, enter the value below.…

A: Substitute

Q: If f(x) x = [²₁ 1 = = then ƒ'(x) = ƒ'(−2) = tadt

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Q: You are stationary on the ground and are watching a bird fly horizontally towards you at a rate of 6…

A: The angle of elevation is denotes by Horizontal distance denotes by x Verical distance denotes by y…

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

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Q: Use the second degree Taylor polynomial for x at x = 8 to estimate 10. Round your answer to four…

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Q: (b) Isolate дет 11 2x 5 = 1/2gt²2² + vt

A: To isolate  in the following equation.

Q: Find dy/dx by implicit differentiation. Then find the slope of the graph at the given point. tan(5x…

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Q: Answer the following questions for the function f(x)=x√x² + 36 defined on the interval -4 ≤ x ≤7.…

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Q: Find the vertex, focus, and directrix of the parabola, and sketch its graph. (x - 6)2 = 2(y + 4) = 0…

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Q: Solve the equation. 7 X-4 X = 5 2x²5x- 12 X 1 2x + 3

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Q: The population P (in thousands) of Tallahassee, Florida, from 2000 through 2018 can be modeled by P…

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Q: If 1800 square centimeters of material is available to make a box with a square base and an open…

A: Let the side of the square base = x cmLet height of box = y cm

Q: For the following integral, (a) sketch the corresponding area, (b) approximate the area using the…

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