The slope of the tangent line to the curve y = 4 X at the point 5, is: The equation of this tangent line can be written in the form y = mx + b where: m is: b is:

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, f'(1) = 1, g'(1) = 5. For the following…

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Q: Determine the following indefinite integral. S dx x√√81-x 18

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Q: For the differential equation y(n) + p₁(t)y(n-¹)+...+Pn(t)y = 0 with solutions y₁, ·, yn Abel's…

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Q: (a) Find the domain of the following function, giving you answer in interval notation. f(x) = ln(x²…

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Q: Find the equation of the tangent line to the graph of the function f(2)=√1026 +26 at the point…

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Q: 1. Sketch the graphs of x = 6y-y² and x = y² - 8. Shade the region bounded between the two curves.…

A: We want to find the area of region bounded between the given curves

Q: 5. lim 248 100 5+2³+ [In(In r)] 7² +6²+ [In(In x)]200

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Q: Evaluate the function at the given values of the independent variable. Simplify the results. f(x) =…

A: The given function, fx=6x-1

Q: Integral Calculus  (Please write the complete solutions. UPVOTE WILL BE GIVEN! NO LONG EXPLANATION…

A: Volume of solid using shell method

Q: f(x)=4 sin¹+x+√4x²

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Q: Find the x-values (if any) at which is not continuous. Which of the discontinuities are removable?…

A: topic- limits and continuity

Q: Consider the following function: f (x) = x^4 − 8x^2 − 8 Determine f′(x) and f′′(x).  Determine where…

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Q: From this graph, Find the volume around the X-axis (Use π = 3.14). y = x (0, 0) (1, 1) y=x² R

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Q: = sin (5√) at the point (7²,0). Enclose numerators and denominators in parentheses. For example, (a…

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Q: Evaluate the integral using the following values. 6 6 6 [°x³ dx = 260, ["x dx = 10, [° dx = 2 + 6 (³…

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Q: Let X 1 f(x) = √²/² 0 e²x² 842 dt. t4 +5 ex none of the choices e2x Find the derivative f'(x).

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Q: Find the mass and center of mass of the lamina bounded by the graphs of the equations for the given…

A: Given-

Q: The limit is equal to 1312 Select one: O True O False lim n→∞ 3n 2n³ + 1

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Q: - lim x²ln x x->0+

A: Solution of given question is written in below steps.

Q: The Normal line at the point (0, –1, 1) to the 3 surface exy - xy² + z³ = -2 is 7=y+1=² Select one:…

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Q: Find the following limits (if they don't exist write DNE, ∞ or -∞ as appropriate): Answer: x-1 lim…

A: We need to find the limit limx→∞ x-12x2-7x

Q: Evaluate. limx---> 0 tan x - x/ x^3 show the steps in paper

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Q: In Exercises 1-2, let u = (3, 2, −1), v = (0, 2, −3), and w = (2,6, 7). Compute the indicated…

A: Note:- according to the company policy we can attempt only three subparts of a question so please…

Q: 9. (a) Express 2 x4 – x² as partial fractions. (b) Hence, compute the exact value of the following…

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Q: Find the tangent line(s) to the parametric curve given by x =

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Q: Find the distance of the point (2, 6, 4)  from the x-axis by two methods

A: To find the distance between the point.

Q: A rectangular piece of cardboard measuring 10 in by 14 in is to be made into a box by cutting equal…

A: The volume of the box is vx=4x3-48x2+140x on the interval 0,5 we have to find its maximum volume…

Q: Consider y=(3x^(2) +4)^(-5x)  Please find dy/dx and evaluate y'(0)

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Q: 3. Sketch the graphs of the curves y = 2x² + 1 and y=7-x. Shade the region bounded by the curves.…

A: We are authorized to answer one question at a time, so we are answering the first one, please repost…

Q: Find the volume of the solid when the region enclosed by the curves y=x², x=1, x=2, y=0 is revolved…

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Q: Evaluate the limit. 1-x² lim *+1 sin(27x) a) lim b) x+2x² C) lim - - 2x *→(π/2)- (2-) tan r Show all…

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Q: After receiving his first income, Mr. J invested P20,000 in a bank for his future family. The annual…

A: This question can be solved by applying the concept of compound interest.

Q: Find the derivative of f(x) = = 30 6/4x+1 Enclose numerators and denominators in parentheses. For…

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Q: Find an equation for the surface obtained by rotating the line z = 7y about the z-axis.

A: On solving this we will get

Q: An $82,000 business can be purchased by making a down payment of $17,000 and financing the balance…

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Q: Three different forces act on an object. They are: F₁ (8,5) (1,7) F₂ F3 (0, 3) = - = Find the net…

A: The three forces are given as: F1→=8,-5 F2→=1,7 F3→=0,3

Q: Evaluate the derivative of the following function. - f(x) = 18x sinh −1x − 180x2 + 1 f'(x) = 18 cosh…

A: To find the derivative f'(x)

Q: The population of mosquitoes in a certain area increases at a rate proportional to the current…

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Q: y = e²+3 dy dx Find dy dx Type sin(x) for sin(x), cos(x) for cos(x), and so on. Use x^2 to square x,…

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Q: i) Find the general term (an) of the sequence 3e-²,4e¯4,5e¯6,6e-8, 7e-10, 8e-¹2,... ii) Calculate…

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Q: Find the derivative of f (y) 30% In(y) Enclose arguments of functions, numerators, and denominators…

A: To find the derivative of the given function.

Q: (5) (a) For all n € N and a + 0, show that k=1 11 1 1

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Let f and g be functions satisfying that f(1) = 3, g(1) = 4, ƒ'(1) = 1, g'(1) = 5. For the following…

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Q: Find the exact area of the surface obtained by rotating the curve about the x-axis. =x²+²x≤x≤1 3x 2…

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Q: 7. Consider the curve C given by the parametric equations x = cos(0), y = sin(0) cos(0) (a) Sketch…

A: Let's sketch the graph and find tangent of given parametric equations.

Q: Sketch the graph of the equation by point plotting. y = 5-x² -3 X y -2 0 2 3

A: Sketch the graph of the equation by point plotting

Q: 2. Simplify the following logarithms and If possible, write the following as a single logarithm. 1…

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: Find a bound on the magnitude of the error if we approximate √2 using the Taylor approximation of…

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Q: Evaluate the integral, which has irreducible quadratic factors. (Use C for the constant of…

A: We will find the integral.