Let 1. f(x) x+1 Use the limit definition of the derivative to find (i) f'(-4) = (ii) f'(- 2) = (i) f'(1) = %3D (iv) f'(3) = To avoid calculating four separate limits, I suggest that you evaluate the derivative at the point when x = a. Once you have the derivative, you can just plug in those four values for "a" to get the answers.

Q: Find the value of Oa 43 Ob.53 Oc 23 Od 13

A: Given: I=∫0∞e-3tdt   As we know that; ∫eax+bdx=1aeax+b+C

Q: (a).x = 61, y = - 4 + 7t O (r, y) = (0,4) + «(6, 7) ai + bj = 4j + 1(6i + 7j) O (1, y) = (6, 7) +…

A: topic - equation of a line

Q: Q1) Evaluate the following integral using Partial Fractions Method: y = : x³ +x? dx х2 +x — 2

A: Given: y=∫x3+x2x2+x-2dx   We know that; The Power rule: ∫xndx=xn+1n+1+C And ∫1ax+bdx=1alnax+b+C

Q: |x= 8| f (x) = Evaluate the left-hand limit of as X8. 16- 2x O 1/2

A: Given,            fx=x-816-2x as x→8To find : Evaluate the left-hand limit of the given function.

Q: Consider the solid bounded by the planes: =x+y, z=30, x=0, y=0. Determine the volume of the solid.

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Q: Q2: Find the integration by applying substitution method: 7 dX (X – 1)VX2 – 2x - 48

A: Given,             ∫7x-1x2-2x-48dx

Q: Find the equation of the tangent line to y = 7e* at x = 3. (Use symbolic notation and fractions…

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Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

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Q: Q2) Solve the D.E xy(x? + 1)dy - (y? + 1)dx = 0 %3D

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Q: Problem 1: Evaluate the following definite integrals. Sx(x2 + 1)V4- 2x2 – x dx -dx

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Q: 2. Sketch the plane curve by plotting points then indicate the orientation of the curve. x = t2 – 4…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 – y from above inside y = x? ,y = 4 .…

A: Given

Q: Consider ,- (x3+y²). Evaluate dx² O (9x4+6x)e «³+y?) O (6r²+ 3x)e (x³+y?) O (6x4+9x)e (x³+y?) O…

A: I have stated the used formulas in the solution

Q: Find the two x-intercepts of the function f and show that f '(x) = 0 at some point between the two…

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Q: Find the average value of the function f(x)=e" on the interval (0,4) Da 3725 Ob 490 OC 745 Od 186 25

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Q: Vx – 8 = xy + 2

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Q: Which of the following yields the value 3580? O none of the choices (18x+7y)dxdy (18x+7y)dydx…

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Q: Q1/ Estimate f (1.72) from the given data using Newton's Backward Difference Formula: 1.7 1.8 1.9…

A: we will use newton backward difference formula .

Q: Q3) Evaluate triple integral Lyx -y)dz dy dx.

A: Topic = Integration

Q: The radius r of a sphere is increasing at a rate of 2 inches per minute. (a) Find the rate of change…

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Q: ind the point of intersection (xo, yo, zo) of the lines given as: L: x = 2 + t, y= 4+5t, z = 5 +t L:…

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Q: 4 4-y Q3) Evaluate triple integral , S S dz dy dx

A: I have stated the used formulas in the solution

Q: 1. S cos (3 sin x)cos (4 sin x). cosxdx sec*x dx 2. Jtanx 3. Sr 6 tan*x dx 4. /2 sin5x dx

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Q: dx = x(1 – y) dt dy у(х — 1) dt

A: Solution of the problem as follows

Q: 0.125 А. f(8t) dt | 0. 0.25 B. f(1 – 4t) dt = 2.5 c. f(5 – 2t) dt =

A: Given that,

Q: Find al ales of that satsy th equation f(x)= g'(x) # f(x)=sin x and g(x)=cos x. 3mt x+kT, where k is…

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Q: Q1: Find the integration of : (choose 3 only ) 1. Sc (3 sin x)cos (4 sin x). cosxdx Cos

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Q: Consider the series 5 + 9 + 13 + How many terms does it take for the sum to be 860? O 21 O 20 O 19 O…

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Q: Find an equation of the sphere whose diameter is the line segment having endpoints at (6,2, –5)

A: To find the equation of sphere.

Q: Determine the equation of the tangent to the graph of y=x - 3x +x+3 at the point (- 1, -2). y 10x+ 8…

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Q: Find the value of e which is defined as the angle between j+k and i+j_ None of the choices 4 프2 프3

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Q: ) Oppositely directed to v = (15, –18) and half the length of v. w = (?, ?)

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Q: 2n br 3n

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Q: Evaluate s 2°ds Oa 2 (sln2-1) (In2)2 2" In2 Oc sin2-1) (In2)2

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Q: If u.v.w are three vectors such that each is inclined at an angle of " with the other two, and that…

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Q: Determine the area of the circle whose center is at the origin and tangent to the parabola y = x2 -…

A: y=x2-100from the grapph attached, Parabola cuts X-axis at (10,0) and (-10,0)

Q: 3. Find the area of the band cut from the paraboloid x² + y? – z = 0 by the planes z = 2 and z = 6.…

A: Let's find.

Q: Evaluate the following integral using Trigonometric Substitutions Method: dx y = 9x2 + 16

A: We will use simple Integration rules to solve this question.

Q: Find the points on the curve y= (x-1)(x -4) where the tangent line is parallel to y= -4x, O (3, 10)…

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Q: Each of the regions A, B, and C enclosed by the graph of f and the x-axis has area 6. Find the value…

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Q: n+1 n+1

A: As per the instruction, we will be answering only the first one. For (1),     limn→∞…

Q: Q3) Evaluate triple integral f , (x2 -y²)dz dx dy.

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Q: 3. Determine the following a A negative angle in radian measure coterminal to Show calculation steps…

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Q: B. Evaluate the following 1 dx 2. 2 tan(x)dx 3.

A: We have to slove above question

Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

A: Here we have to use the trigonometric subsitution method.

Q: F'(x) = (ax3 + b)2 O none of the choices O 1 За ах3 + b 1 1 2a ax3 + b 1 1 - За аx3 + b. o 1 2a (…

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Q: Solve the particular solution of the equation dy/dx = 3x² - 2x, when y=2 and x=-1.

A: We can solve the given problem as follows:

Q: 6.Find all the first partial derivatives of each function x² – y² c. f(x,y) ху с. = d. f(x,y)=e* cos…

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Q: The limit represents a derivative f'(a). Find f and a. V3 sin (5 + h) lim 2 h→0 h (Express numbers…

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Q: n(A U B) = 55, n(AN B) = 15, and n(B) = 35 %3D Find the value of x A 15 y

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