Prove that: sec (0) +tan (0) cot (0)-cos (0) -=sec (0) tan (0)

Q: D In10 In[log(x+1)] + C

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Q: The concentration C(t) of a certain drug in the bloodstream after t minutes is given by the formula…

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Q: Consider the following. (Round your answers to four decimal places.) f(x, y) = x cos(y) (a) Find…

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Q: 70. If A = (4i-3k) and B= (-i+j-2k). Find the vector product of A and B. a. (6i+8j+k) b. (-6i+8j+7k)…

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Q: || + 3 вн f(t) dr = 3 f(t) +

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Q: the derivative of the function by the limit process. f(x) = x²+x-3

A: Topic:- limits and calculus

Q: Graph the function by setting the moving points correctly. Provide your answer below: -10 -5 (-3,0)…

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Q: Find the derivative of the following functions. 1. F(x): = ſª √³+8dt

A: As per Bartleby guidelines rule I am answering only first question as other questions are not the…

Q: 2 i) [x² ( x + ²7 - 2²/1) dx x i) Ï 0 x³ - 8 x-2 dx ii) ii) f (x³ + 3x² + 1) e-2x dx xe xe1+x dx

A: Given:   i) ∫x3x+2x-1x2dx Expand   =∫x4+2x2-xdx Apply linearity     =∫x4dx+∫2x2dx-∫xdx

Q: Find an equation of a line that is tangent to the graph off and parallel to the given line. Function…

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Q: dy dx -5y=-tr, 5y = ³ 2 y(1)=1

A: The given differential equation is  dy/dx -5y= -5/2 xy3 , y(1)=1

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Formula:

Q: A tank initially contains 10 kg of salt in 50 liters of water. Pure water enters at a rate of 2…

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Q: 62. A bacteria culture has an initial population of 500. After 4 hours the population has grown to…

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Q: mine the area of the given region. y = x + sin x 4 X 4 A 3 2- +

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Q: 7. y = tan³ (2³) (A) 3x² sec(2³) tan(x³) (B)-3x2 sec(³) tan(x³) 8. y = cos(5x) (A) sin(5x) (B)-5…

A: Topic = Derivative As per guidelines, At a time only three sub-parts of a question can be answered.

Q: Use cylindrical shells to find the volume of the solid obtained by rotating the region bounded on…

A: The given data is: gy=8y To find: the volume of the solid obtained by rotating the region bounded on…

Q: Give the applicable trigonometric substitution formula for S A. x=2 sin 0, dx = 2 sec ² 0 de B. x…

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Q: 6) Find the domain of the given functions (use interval notation) and the find f(g(x)) f(x) =…

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Q: 10. Consider the piecewise function (with the piecewise having TWO pieces). Find the piecewise…

A: We need to find piecewise function.

Q: Use the product rule to find the derivative of y=(5x² − 4)"^(2x* + 7)³³ NOT Simplify after…

A: This question is related to differentiation, We will solve it using given information.

Q: S: z = √x² + y², (x-1)² + y² ≤ 1

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Q: Graph the integrand and use areas to evaluate the integral. 5 S (5-1x) dx -5 A. 50 B. 75 C. 25 - 2…

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Q: The tangent line to the graph of y = g(x) at the point (9, 1) passes through the point (4, 6). Find…

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Q: The graph of f is shown. y -10 0 10 y = f(x) 20 30 40 X

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Q: Please find all 0 ≤ 0 ≤ 2π, for which ... (a) tan () = √3 (b) 3 sin²(0)+ 4 = 5 (c) 2 cos(ln(x² + e²)…

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Q: Find anti derivative of    3cos(x)-7x4+2x5

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Q: Graph the function given below by moving the vertical asymptote, then the value of the -intercept.…

A: Let's draw the graph.

Q: 4. Find the following limits: (a) (b) 2 lim-3 x-3 - 2 4 3-x 12x - 4x² lim x3+x² - 6x +9 1

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Q: Find the volume of the solid obtained by rotating the region bounded by the curves y = x3, x = 9,…

A: We have to find the volume of the solid obtained by rotating the region bounded by the given curves.

Q: Find the absolute extrema of the function on the closed interval. f(x) = cos TX, [] minimum (x, y) =…

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Q: Prob. 6 (a) 3) Find the critical numbers of the function y = x³/2 - 4x¹/2 3

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Q: Describe the x-values at which is differentiable. f (x) = { 3²-7 x²-3x≤0 3-x²x>0 T -2 2 -2 The…

A: Let's find function is differential or not.

Q: Evaluate the following integral: S₁ S² == dydx −1 1 y

A: Given integration: ∫-14∫1ex2y dydx

Q: Use the Ratio Test to determine whether the series is convergent or divergent. Identify an Since lim…

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Q: Determine the point(s) (if any) at which the graph of the function has a horizontal tangent line.…

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Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = L{f(t)} and n = 1, 2, 3, . . .…

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Q: 1 ) [ x (x ² − ² + + + + ) dx i) - x

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the derivative of the logarithmic function. f(x) = 2x² In 2x f'(x)= 4in (2x) + 6

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Q: The direction of the graph of the given function and by what factor the function is to be stretched…

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Q: Find F(s). F(s) = £{t(et + e5t)2}

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Q: When reduced to a linear DE of order one in z, the Bernoulli's equation dy 2 +y √( 1 ) = 3x²y² =…

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Q: Consider the following double integral 1 = ₂ x dy dx. By converting / into an equivalent double…

A: Given :- I=∫-33∫-9-x20dydx convert given integral to polar conversion

Q: ) . Solve the differential equation by using integrating factors. xy' = 6y + x2 y(x) =

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Q: The limit represents f '(c) for a function f(x) and a number c. Find f(x) and c. 6 √x - 30 x - 25…

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Q: Find the area of the region bounded by the graphs of the equations. Use a graphing utility to verify…

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Q: Use the given information to find the exact function value. Simplify your answer as much as…

A: The given sinθ=25, tanθ>0 . We have to find the values of cos2θ and sin2θ

Q: (5) f (3x² + 2x)e5+3x dx (6) ſ dx x(3 + ln x)

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Q: what

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Q: 2 3 [²³x²³ ln(x¹) dr Sº x exp(-x) dx 1 X Jo 2x² +1 dx

A: Solve the integral