Consider the following. Find f'(t) and g'(t). f'(t) = g'(t) = f(t) = t sin(t) g(t) = 1 + t Differentiate. y' = y = t sin(t) 1 + t

Q: 24. Let W be the amount of water, in gallons, in a bathtub at time t, in minutes. At t = 0 water…

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Q: 23. lim 848 5√√x+3 1 - 17x²

A: Solve limit

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Q: X 16. Determine the equation of the tangent to the curve y=30* at the point with x-coordinate.

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Q: 14. √9-x² x2 S dx

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Q: Find the value of a that makes the following function differentiable for all values of x. g(x)= ax…

A: According to question, Given Function,gx = axif x<0x2-7xif x≥0

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A: The given curve x=t3-3t, y=t2-4. We have to find the points on the curve where the tangent is…

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Q: a) which of the following is the graph. of y = X² ex # B) 2 of 44 c)

A: Shown below...

Q: Enter the equation of the parabola graphed below, using the vertex form y = a (x-h)² + k -5 -4 -3 -1

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Q: The given point is on the curve. Find the lines that are (a) tangent and (b) normal to the curve at…

A: standard form of line is y=mx+c,  where m is slope dxndx=nxn-1d(constant)dx=0

Q: EC: Find the derivative of g(x) (x) = = 0 cos(t²) dt cos(1¹) di

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Q: The graph of f is shown below. Evaluate each integral by interpreting it in terms of areas. 1 So…

A: we need to find out the given integration by interpreting in the areas.

Q: Find the point on the graph of the function f(x) = √x that is closest to the point (30, 0). 59 (2)…

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Q: 4- Say whether each given sequence is a geometric sequence, or not. Find the common ratio and the…

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Q: Determine the general solution of the non-homogeneous differential equation y + y = sinx.

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Q: 3. R is the region between f(x)=xln(x) and the x-axis on the interval [1, e]. (a) Write an integral…

A: Since you have posted multipart question i can do first three subparts as per our company guidelines…

Q: Find the absolute maximum and minimum values of the following function on the given interval. Then…

A: Please see the below picture for detailed solution.

Q: Evaluate the integral 4x3 x² +1 - dx.

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Q: Find f such that f'(x) = 8x² + 7x-7 and f(0) = 2. f(x) =

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Q: In the accompanying diagram of a unit circle, the ordered pair (x, y) represents the point where the…

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Q: rivatives · [²32²³ + 1 dr = es. Show all work 14.

A: Given query is to find the integral.

Q: Let f(x) = sin(z))". Find (1). (1).

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Q: X Find the point of inflection of the graph of the function f(x)=2sin on the interval [0, 147]. ○ (7…

A: Given query is to find th point of inflection.

Q: Referring to the graph of f shown, use the graph to determine the value of the definite integral. S…

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Q: A right triangle has an area of 20 square centimeters and a hypotenuse of 10 centimeters. what are…

A: Solve the following

Q: Use area to evaluate the integral 7x • ! 0 dx = dx, b>0. ...

A: NOTE: Refresh your page if you can't see any equations. . the given function is  which is the…

Q: 8. Determine 16 25 a. b. 4 25 dy dx y = for x²-4 +4 when x 1. Show your work. c. 16 25 d. 1

A: The given function is: y=x2-4x2+4

Q: If lim X-5 f(x)-8 X-4 lim f(x)= X-5 = 1, find lim f(x). X-5 (Type an integer or a simplified frac

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Q: 1 x 69. g(x) = ₁ ₁³ + 14 dt 3

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Q: d) xy' + (1+x)y=e* sin(2x)

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Q: Transform the given differential equation into an equivalent system of first-order differential…

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Q: Which of the statements a through i about the function y = f(x) graphed here are true, and which are…

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Q: 2. What is the slope of the tangent to f(x)=√√x-1 at (5,2)? Show your work. a. 1 C. 2 4 b. 1 2 d. 4

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Q: Suppose that a is the area of a disc with radius r which is expanding in time t measured in seconds.…

A: Given a is the area of a disc with radius r which is expanding in time t measured in seconds.   We…

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A: we need to write down the equation of ellipse from the given graph.

Q: Determine whether Rolle's Theorem can be applied to the function f(x)=x²- 10x + 16 on the closed…

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Q: 5) Find the divergence of (√x² + y² + z² 5) kî + yî yj + zk)

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Q: Given the following data, calculate b, of the quadratic New difference polynomial: f(x)=0 f(x₁) =…

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Q: If ["F(x) 1.2 f(x) dx = 7.2 and nd ["fix) dx = 5.6, find [° F(x) dx. X

A: we know that ∫abf(x)dx=∫acf(x)dx+∫cbf(x)dx, where c is betwwen a and  bgiven  ∫17f(x)dx=7.2 and…

Q: 15. [cost dr =

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Q: Find solutions to the equation 5 Tan²x + Tanx = 2 on interval [=17, 27). Round Solutions to 4…

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Q: 18) The graph of f(x) is shown. fox A) I only 4 B) 1:4 f¹=0 at X = ? c) 1; 4; 5: D) 143536

A: As per guideline only one question is allowed to solve if multiple question is asked in single…

Q: Consider the following matrix. 3 0 19-3 62 13 44 1 8 8 30 12 0 0 00 (a) Find the dimensions of the…

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Q: 3) Find curl (xyi + yzj + zxk)

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Q: Sketch the curve. r = 9 cos(8) O -4 ac -2 O y 2 -8…

A: Given query is to sketch the curve and find the area.

Q: At time t, the position of a body moving along the s-axis is s = t³ - 9t² +24t m. a. Find the body's…

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Q: If y is inversely proportional to x, and y = 9 when x = 6, write a formula for y in terms of x. Use…

A: Given y is inversly proportional to x let k = proportionality constant

Q: Find the area enclosed by the curve x = x = t² - 2t, y = √t and the y-axis.

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Q: The region between the curve y = √x, 0 ≤ x ≤ 4, and the x-axis is revolved about the x-axis to…

A: Given y = x0 ≤ x ≤ 4 as we know that volume pf solid bounded by revolution of y = f( x ) V =…